Opening remarks / Christopher A Fuchs: QM as quantum information (& others)

0:00 I hope he goes well. Thank you for your attention. You don't actually have a stick. Or you could use Paul's crutches. But they're a bit big. You should get one of those laser things. Oh, I hate those. Do you have any shake in your hand? The whole audience. Thank you for your attention. Thank you for your attention. So, so, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did, you did,

2:30 Excellent. Hey, hello. How are you? Nice to see you. Nice to meet you. Yeah, I was preparing my talk. That's what I said to somebody. I said, you know, I was too... Up till four in the morning. I wasn't at the... Well, I was, like, I couldn't sleep at the time. So, you were up again. I knew that you were here. I... I... You always do. The funny thing is it doesn't matter when I stop. Yes, you always do. I don't know whether I start a week before or two days before then. It's crazy, there's some kind of more to this stuff. But anyway, we must remain friends, whatever happens. Thank you for your attention. Thank you for your attention. So, you guys have a clear idea of what you're going to be doing in the future, right? Well, I don't know if you guys have a clear idea of what you're going to be doing in the future, right? I don't think so. So, you guys have a clear idea of what you're going to be doing in the future, right? I don't think so. So, you guys have a clear idea of what you're going to be doing in the future, right? I don't think so. So, you guys have a clear idea of what you're going to be doing in the future, right? I don't think so. So, you guys have a clear idea of what you're going to be doing in the future, right? I don't think so. So, you guys have a clear idea of what you're going to be doing in the future, right? There are a number of different fields of study, including mathematics, geometry, algebra, mathematics, physics, physics, and mathematics.

5:00 There are a number of different fields of study, including mathematics, geometry, algebra, mathematics, physics, and mathematics. There are a number of different fields of study, including mathematics, geometry, algebra, mathematics, physics, and mathematics. There are a number of different fields of study, including mathematics, geometry, algebra, mathematics, physics, and mathematics. There are a number of different fields of study, including mathematics, geometry, mathematics, physics, and mathematics. There are a number of different fields of study, including mathematics, geometry, mathematics, physics, and mathematics. Thank you for your attention. Thank you for your attention. Thank you for your attention. Thank you for your attention. I mean, I got a couple emails from Japan, but when I responded, I'm sure it's up. Thank you for your attention.

7:30 He didn't respond. We're going to do it all the time. But they're not going to come out all the time. Thank you for your attention. Thank you for your attention. Thank you for your attention. There are a number of different fields of study, including mathematics, geometry, algebra, mathematics, physics, physics, and mathematics. There are a number of different fields of study, including mathematics, geometry, algebra, mathematics, physics, and mathematics. There are a number of different fields of study. Okay, good morning everyone. We should probably make a start. Okay, my name's Chris Simpson from the University of Leeds.

10:00 And I'd like to welcome you all to our workshop this morning on quantum information theory and the foundations of quantum mechanics. We're hoping to address the question, get some handle on the question, whether information is the way forward in quantum mechanics. There's also the thought that there's a strong current of feeling amongst workers in the area in quantum information theory that The developments in their field are going to shed some important new light on the nature of quantum mechanics itself, and perhaps even on the nature of the world we live in. Now that's the sort of issue that philosophers of science should be very interested in looking into, and so that's our aim today. Now, one of the difficulties with this sort of investigation is that Although this current of feeling that there is something to be said coming from quantum information theory is a very strong current of feeling, it's rarely been expressed in very concrete terms. The thought is present, and it's the sort of thought that's present in the conclusion and the introductions of papers, but doesn't seem to appear that much in the middle often. But today we're lucky enough to have with us two people who have been instrumental in making more concrete proposals and actually trying to get something concrete out of these more vague thoughts. And so I'm talking about Chris Fuchs from Bell Labs and Geoffrey Book from the University of Maryland, who have been well known to many of you. Geoff and Chris have, as I say, both actually made concrete proposals about how we should understand the impact of quantum information theory in revising our views on quantum mechanics. And they're going to be talking about those today. Now the issues are somewhat controversial, and so to have a balanced... In this forum, we're very pleased to have with us Anthony Valentini from the Primm-Ritter Institute to argue against what he sees as wrong or difficulties with some approaches that are based on information in quantum mechanics. So the structure is going to be, I'm just going to introduce with a few opening remarks to set the scene and to deep-view some initial worries that some people might have and hope that we can then move on to more substantive issues that are going to be discussed by our speakers today.

12:30 Then each of the speakers will have 40 minutes including questions to talk. We'll have a brief break after Geoff's talk is coming second for you guys to refresh yourselves. We'll come back and have Anthony's talk and then we'll move to a discussion period. I'm hoping to have quite an extensive discussion period around half an hour, 35 minutes or so. We'll start off with a discussion amongst our panellists which will be led by Ari Duell from the University of Pittsburgh in Constance. He's going to be leading up the discussion and at that point, once the speakers have finished tearing strips off each other, you can get your turn too, and I'm here to kind of keep things in order, I guess. Right, so the opening remarks. I had this quotation up at the beginning. This is from Shannon. Being philosophers of science, we want to start off with a suitably analytic and... This is a clear-headed approach to the question of whether there are any cases to be drawn from quantum information theory. And I think this quotation from Shannon expresses very nicely the suitable sort of careful attitude we should be beginning with. So this was a comment in the mid-50s when there was... You know, the Shannon papers were in 1948 and there was a great explosion of interest in many fields in information theory, and Shannon made the valid point that a lot of these implications that were trying to be drawn from classical information theory were somewhat overblown. So he says, information theory has in the last few years become something of a scientific bandwagon. Although this wave of popularity is certainly pleasant and exciting for those of us working in the field, it carries at the same time an element of danger. While we feel that information theory is indeed a valuable tool, it is certainly no panacea for the communication engineer for anyone else. Seldom do more than a few of nature's secrets give way at any one time. It would be all too easy for our somewhat artificial prosperity to collapse overnight when it is realized that the use of a few exciting words like information, entropy, redundancy do not solve all our problems. So that seems to sound intriguing. Warning when moving into the quantum information literature, we need to not get overexcited by this word information, which is a bit of a weasel word at some points, has many different senses, used in various different ways, and is frequently not sufficiently distinguished or articulated.

15:00 That was Shannon. On the other hand, we should balance this with a quotation from Fuchs, from Chris here. No tool could be better calibrated for a direct assault on quantum foundations than quantum information theory. Far from a strained application of the latest fad to a time-honoured problem, this method holds promise precisely because a large part, but not all, of the structure of quantum theory has always concerned information. It is just that the physics community needs reminding. And that's what he's going to be trying to persuade us of today. But before that, as I said, there are a few sort of fairly elementary points to be made if we're going to, I think, make a worthwhile assault on understanding. The idea that appealing in some form to a notion of information or knowledge is going to help us with quantum mechanics is the sort of idea that's appeared at fairly regular intervals over the years, particularly amongst those in the Copenhagen tradition. The thought, roughly speaking, is that there's sort of a sketch of how the view is often articulated, saying something like, look, you get yourself into problems interpreting quantum mechanics if you take the quantum state too seriously, if you take it to be a real thing describing objective properties of systems in the world. Now, if instead you consider the state as being, say, a state of knowledge that we have or the information that we have about a system, rather than representing how the system is. Then one can avoid these problems, right? You can avoid the problem of measurement because it doesn't matter that sometimes the quantum state jumps in a funny way and sometimes it moves in accordance with the Schrodinger equation. Because, you know, the funny jump is just happening when we're updating our information. You look out into the world, see something, okay, we update the information that we have about a system. There's not physical systems jumping around in peculiar ways or their properties varying, sometimes deterministically, sometimes indeterministically. What's varying is our knowledge about a system, okay, so one tries to blunt the measurement problem in that way. Similarly with the problems with non-locality, right, so if you have Alice and Bob sharing a single state, normal sort of scoring, Alice performs her measurement, pure state jumps out on Bob's side when before it was a maximally mixed state.

17:30 Now, according to someone who's saying that information is what the quantum state is, or what the state represents on knowledge, that change from the mixed state to the pure state on Bob's side isn't a change in the physical properties of the system on Bob's side. It's not a non-local change. It's not a non-local causal effect. It's merely a change in Alice's knowledge about what she can say about Bob's system. Types of solution that tends to ameliorate the conceptual difficulties. It's an important point, it's a very important point that two different people can assign different states to the same system. Okay, so consider the Wigner's friend example. This would be pertinent in a measurement problem case. The person inside the lab doing the experiment on the system assigned one state to that system. He knows, he's seen that it's collapsed, he gives it some pure state. Wigner on the outside assigns just some entangled state to the joint system, so that means that Wigner and his friend disagree or fail to agree on what the actual pure state of the object system is. But that doesn't matter because the state isn't representing properties of the system, it's just representing knowledge. Similarly, in the non-locality case, Alice... Bob's system is in some pure state. Bob says, no, it's not. My system is still in some maximally mixed state and the maximally mixed state. So they're ascribing different states to two. Two people are ascribing different states to the same system. But again, it doesn't matter because they're not ascribing different physical properties to one and the same system. That's an important point. That's the sketch. Sorry, I'm taking it too long. What should we do with it? One avenue of approach is to go via Bell, right? The great John Bell who always had very profound things to say about quantum mechanics. And, of course, information is on the famous list of bad words, you know, as reported in the paper against measurement. It's one of those bad words that have no place in the formulation with any pretense to physical precision. And the problem here, Bell articulates via two questions.

20:00 If the state is information, or if it's knowledge, it's information about what? And whose information is it? And these are very good questions. In particular, the first one. That's the one I want to focus on. Because I think this presents a very strong difficulty, which I call the cilia and charybdis, for information talk in quantum mechanics. Because consider that there are two possible answers one might give to what the quantum state is information about. It could be information about what the results of experiments will be, or it could be information about co-existing values living in the system. So, in the former case, if it's information about what the results of experiments will be, then we're having a difficult time distinguishing the appeal to information from simply being a form of instrumentalism about the quantum state. If it's the second case, information about these pre-existing values, then we're simply talking about the hidden variable theory. And the proponents of information shouldn't be happy with having to move to the hidden variable theory, because the thought was that by making this quantum state represent information, you're going to get better behaved things, you're not going to get funny jumping around, you're not going to get funny null local. If you're being forced to say that actually it's information about hidden variables, then the hidden variables are going to be very badly behaved, indeed, non-local, non-contextual. So that avenue is not successful. So if we move away from the hidden variables, then the difficulty is saying, well, is appealing to information any different from simply being instrumentalist? Warning is pertinent, right, because it might sound like an interesting new doctrine to say the quantum state is information, but really if that's just an old thesis in new clothes, that doesn't make the old thesis any more acceptable than it was before. It doesn't make it any less acceptable, right, so if you're happy with an instrumentalist view, that's okay, but it certainly doesn't make it any more acceptable. That's the one point. I'm going to make the second point about factivity. Okay, sketch what the point of trying to appeal to the state being information was. We thought we could get around the measurement problem. We thought we could do something about non-locality. But, unfortunately, the words information and knowledge,

22:30 the concepts information and knowledge, don't seem at all to be the right sorts of concepts that are actually going to do that job the person wanted them to do. For the simple reason that information and knowledge are both factive So you can't know that P unless P is the case, unless P is true. You can't have the information that P unless P is true. So that means that this spells difficulty, or it's an unavoidable difficulty that can't be resolved for the person who needed to say that I'm solving the measurement problem by allowing more than one state to be assigned to a given system. Because if information and knowledge are factive, then if Alice knows that Bob's system is in some pure state, psi, then that system sure is in the pure state, psi. There's no ifs, buts about it. And Bob is simply wrong to assign his different state. Similarly in the Wigner's friend case, there's no scope for saying, okay, there's not any real disagreement here. So you can't, by using information and knowledge, actually solve the problems in the way you thought that you could, because these concepts are factive, and that forces precisely the form of objectivity that you'd hope to avoid by appealing to information. So you're going to have to do something more clever. There are more clever things one can do. And at that point, I should hang over to Chris who will explain what those are. That's the one thing I'm not going to talk about. Yes, Lee? That would be good. Quantum mechanics is quantum information and only a little more. I liked it when Chris was reading the abstract or something from one of my papers where he said, what was the quote? New tool. Mr. Campbell, whatever. Where he said, very nice. Far from a strained application of the latest fad of time to a time-honored problem, this method holds promise precisely because a large part, but not all, these are great columns.

25:00 You should say, but not all. That's the important part. So quantum mechanics is something about information, but it's not all and only about information. That's what this talk is going to be about. You can read about all of this on one of my papers on the Los Alamos archive, which may not discuss everything, but at least it has references to everything. Well, quantum information and quantum computing is a subject matter that the U.S. military and the National Security Agency is quite interested in, and they're interested in it predominantly because it can help us communicate secrets secretly, and it can allow them to break into secure communications, so they're one of the reasons. We've discussed this at quite length, is that A lot of people now in the quantum foundations community have taken to looking at quantum information to see if it has any implication on this aspect of quantum mechanics. And there's been quite a bit of activity. This is something I drew up a few months ago, but since then, for instance, Chris has his PhD thesis on the subject. Ernesto Gambayo has a PhD thesis on the subject. One of Jeff's students has a master's thesis on the subject. So there's been a lot of activity. What I think is exciting is that I think for the first time we have the possibility of breaking what I think has been an impasse in quantum foundations in the last 75 years that I'd like to illustrate by this poll that Max Tegmark drew up a long time ago, maybe not so long ago. And I think it illustrates especially something from when I had my first conversation with Lucian Hardy. Everybody knows about Lucian Hardy and quantum foundations. So the first time I was talking to him, I said, how do you know when you've made progress in quantum foundations? And Lucian said, it's not a question we ask. Well, you can kind of see that in this poll because at best, as far as I can tell, looking at the proceedings from quantum foundations meetings over the years, you see the number of supporters for any given interpretation just fluctuate. It goes up, it goes down, but where's the real progress?

27:30 In my own view, the only way we're ever going to make real progress is if we do something like the following. What quantum mechanics is, as it's presented, say, for instance, in a textbook, it's usually presented axiomatically. You're told that systems, well, associated with systems are these complex vector spaces, that measurements correspond to her mission operators, or you might say orthonormal bases, that the states are vectors on these spaces, and so forth. I think the only direction for progress that we have is if we can take this structure, quantum mechanics as it's usually presented to us, and to do something with it that's much like what Einstein did with Lorentzian electrodynamics. He looked at this rather unwieldy structure of Lorentz transformations and was able to distill from it Two very crisp physical statements, that the speed of light is constant and that physics should be the same in all inertial frames, and he was able to take these two very crisp physical ideas and from them reconstruct, you know, the elaborate mathematical structure of Lorentz transformations. Well, at that point something new happened, something good happened, and you could see a direct line to progress. This very mathematical, non-physical looking structure, and somehow replace it with something that's more of the flavor of that. Well, that can't be the end point, at least not in my own opinion. I think that's actually just the starting point. And what we're striving for now is to get to the starting point. Where the sparks really flew after Einstein's re-massaging of special relativity was when he was able to take these principles, or maybe better yet, maybe I should give Minkowski all the credit. When he was able to take these principles and look into them and find the essential, I would say, ontological content of these principles. So we went from this very operationalistic set of assumptions, C is constant, physics is constant, and turned that into Minkowski's space time.

30:00 The sparks then came just a few years later when he started exploring the idea of how to incorporate gravity into this picture and then, you know, this great insight to take this space-time linear curve. And all of a sudden you have new physics. Well, this is what I hope we will find in this quantum foundational search, that we'll be able to take quantum mechanics, distill it to a few key principles, figure out the essential content, what they're saying about the world as it is, independently of all of us, the world that was here five million years ago, the world that will be here five million years later. Get the essential ontological content of the theory and at that point you can see what to do with it and it's not just wild speculation as I might call let's say GRWBs or Bohmian mechanics, sorry Anthony, things like that. So how might we go about trying to get that? My own opinion, and of course the talk is going to be about my own opinion, is that We need to just be upfront and swallow the following idea. The quantum mechanics is about information. Not anything exotic, not some kind of new fantastic information with all sorts of wild and complicated properties, but that it's about information in the plain ordinary old Shannon sense of ignorance or lack of predictability. This is the starting point, that we just sort of need to kind of take this and put it into ourselves and see what comes of it. But we have to be careful. We can't go around. Doing things like our colleague Anton Zeilinger in saying, all the world is information, that goes too far. The thing to recognize is that it's about information, but it's only mostly so. There's still some content that has nothing to do with agents and their beliefs or their expectations of anything. So really what I'm saying is that we should take as our starting point something along these very old lines, like Chris Timpson was just talking about. I'll put it up here for part of this thing I call the Tim Hartman 1968 Section 4 interpretation of quantum mechanics. Because, you see, he has this long paper and I could only buy into one section of it, and even then I had to suitably modify it so that I could read it to you.

32:30 So Jim says, a quantum state, being a summary of the observer's information about an individual physical system, changes both by dynamical laws and whenever the observer acquires new information about the system through the process of measurement. The existence of two laws for the evolution of the state vector becomes problematical. Only if it is believed that the state vector is an objective property of the system. If the state of the system is defined as a list of, here's one of my modifications, as a list of experimental propositions together with their probabilities of occurrence, it is not surprising that after a measurement the state must be changed to be in accordance with the new information. The reduction of the wave packet does take place in consciousness of the observer, not because of any unique physical process which takes place there. But only because the state is a construct of the observer and not an objective property of the physical system. So what I'm supporting is that we take this point of view as at least a good starting point for further explorations in quantum mechanics. Now, this may have to be modified, we may have to do some things with it, but the idea is to hold firm to this. And a lot of people do, and even I did, that you better have more reasons than this for taking the quantum state as information. Let me just recommend one paper that I think is the happiest paper I've seen in about two or three years that I like to advertise. It's a paper by Rob Speckens, who's unfortunately not here, that he titled, This is a paper that's not about quantum mechanics. Not at all about quantum mechanics. He invents a little theory that has ontic states and epistemic states. Nothing to do with quantum mechanics, it's just a theory where there are these things called ontic states, states of the world, and there are these epistemic states, what you know about these ontic states. And then he plays with this, with this theory. So let me just read you his abstract, or at least part of it. So he says, we present a toy theory that is based on a simple principle. The number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge.

35:00 So he gives a restriction to the epistemic states. Omni states, epistemic states, on the epistemic states there's a restriction about how much you can know when you have maximal knowledge. But then here's the really interesting thing about that paper. Even though it's not quantum mechanics, he says, A wide variety of quantum phenomena are found to have analogs within display theory. Such phenomena include non-commutivity of measurements, interference, multiplicity of complexity compositions of a mixed state, there's a no-cloning theorem, a remote steering theorem, a teleportation theorem, a kind of quantum cryptography, and the list goes on and on. He has about 25 or 30 quantum information phenomena that are captured by this toy theory, even though it is explicitly not quantum mechanics. He says, is taken as evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to capture. This is the interesting stuff. Violations about inequalities and the existence of approaches. Specker theorem provides clues for how to proceed with a research program wherein the quantum state being a state of incomplete knowledge is the idea upon which one never compromises. So, here's really the line of research laid out straight. There's quantum mechanics, and there are a lot of terms in quantum mechanics, one of which is the quantum state. Before one gets too detailed about what the quantum state is information about, it's just worth exploring in what ways is it like information and what can this teach us. If you can settle and learn something from that process, then maybe the next step is to really tackle this question that Chris brought up, information about what. But that's a secondary question. If we can first settle some issues about the nature of the quantum state, that's already useful. So the picture you should have in mind is something like this. There's a physical system. That little square, and I'll use it over and over, represents the stuff that's out in the world independently of the observer. And I am a realist enough to say that when you kill me, the world will still be here.

37:30 However, there's also this thing in quantum mechanics. The informational point of view about psi is that there's no good sense in which this psi is attached to this little brick. In particular, this psi is better pictured as attached to me, stapled to my head. When I walk into the room and I say, ah, there's a physical system that I want to talk about, then I might pool all of my knowledge, and when I do, I end up with something like this. But when I walk out of the room and I stop considering the system and how I might interact with it, I take this with me. That is not to say that the system there goes with me. If the system went with me, I'd be a solipsist. But I'm not a solipsist. I'm just taking my information. The world as it is out there is still whatever it was. Now, we'd like to get to more than that. What's still in parenthesis that Chris was talking about is ultimately we'd like to know how is this different from instrumentalism. What is it that's real about a system? If the wave function is information, what's real? We'd like to have an answer to this. And now, unfortunately, and it's hard giving talks in front of audiences like this, I have to say I don't know what the answer to that is going to be. There are only two things I can tell you. I can tell you something firm, and that is... That whatever this final statement of quantum theory is, this statement about what's real about the system, it should not involve psi's at all, because psi represents information from this point of view. So what's real about the system, it's going to be some mathematical structure, presumably, or represented by some mathematical structure. But that mathematical structure had better not make any use of wave functions. That's one thing. This is more constructive, I hope. And that is, though I can't presently tell you what is real, what is this zing, this pow, this zip that makes quantum computers run and gives us quantum phenomena, I can at least give you a methodology for trying to pinpoint it. So what is that methodology?

40:00 If we recognize that the quantum state is something like information, or maybe a Bayesian expectation, or however you want to put it, it seems reasonable to ask not only about the quantum state, but all of the superstructure, mathematical superstructure, that supports quantum states. So the analogy is this. It strikes me that we should go back to any statement of quantum mechanics, let's say this set of axioms, and ask for each and every one of these axioms, each and every one of these pieces of quantum mechanics, can we give an information-theoretic reason that it takes the form that it does, or not? Now, we might be able to, and I'm expecting that we can give information-theoretic reasons for a lot of this structure. But we may not be able to give an information theoretic reason for some pieces of quantum mechanics. Well, this is a valuable lesson, I think. We take a piece of quantum mechanics and we ask, can I give an information theoretic reason for it? Well, if I can, I put it on this side of the shelf. If I can't, however, try as I might, I can't give an information theoretic reason, I put it on this side of the shelf, and so forth. At the end of the day, at least we can say this stuff over here on this side of the shelf, the stuff that we can't give an information theoretic reason, stands a chance of being a statement about the world independent of agents, independent of observers, and helps us identify it. And then hopefully, at the end of the day, when all of that is still, we'll have these simple principles that we've been talking about. So here's my plan for the rest of the talk. That lays out the whole philosophy of the program, I hope. What I'd like to do is give a little bit of substance to this game to show you that it does bear some fruit and that you can go to different pieces of quantum mechanics and give something like an information theoretic reason. Now, information theoretic reason loosely comes through. What I really mean by that is something like, can I give a probabilistic reason? Can I give, in particular, my own? Vent toward probability is something like Bayesian. Can I give a Bayesian reason for this or that piece of the quantum mechanics?

42:30 And I want to do it for three things. I'll probably only get through two. One is associated with each of the complex vector space. Can I give an information theoretic reason for that? I think I can. So that's going to be the first thing I want to show you. Systems combined according to the tensor product rule. Can I give an information theoretic reason for that? I think I can. And then finally, the one that I'd really love to show you, because I think it really gets to the nub of the matter, is that measurements correspond to working normal bases. Can I give you an information theoretic reason for that? I'd love to show you that. And I can show you that, but that's probably going to have to wait until either the discussion or the next talk. Well, to start exploring that, let me bring you to an issue of something that happens over and over in quantum information theory, and that is, for almost any paper that you pick up on the archives, you'll find the phrase unknown state. They're all over the place. There's something called the no-cloning theorem that says you cannot clone an unknown state. You teleport unknown quantum states. You protect unknown quantum states with quantum error correcting codes. This is the big technical innovation that's going to allow quantum computers to run. But how much sense does this phrase, unknown states, make? Well, if you take an informational point of view about quantum states, it doesn't seem to make any sense at all. Because what are we talking about here? Suppose we've got this system right there, and there's this observer out here, and he says, the system has an unknown state. So we're going to put it into a quantum cloning machine or something like that. Well, what can he mean? If he's accepted the informational point of view about quantum states, you would think, well, maybe the only thing he can mean is that there's somebody else out there. There's this guy up here. And he has some state that he's written for this system, and he just doesn't know it. Well, that seems like a strained way of going about trying to define the notion of what an unknown state means.

45:00 So much so that you might say, well, how can I even define all of these phenomenons without always inserting an extra observer, and is it that really, at the end of the day, you need observers always in the universe just to kind of keep quantum mechanics from collapsing, or to make sure that when there's no one about in the plot, there will be free spaces? Well, let me make that even sharper. One of the things we often talk about in... Quantum information is calibrating instruments, and there's a process called quantum state tomography that is used for calibration. The idea there is you have a big preparation device, let's say like a laser, and this laser sends out pulse after pulse after pulse, and you've got the experimentalist in his laboratory, and he would like to characterize this laser. One is usually presented as, here's this device, and it prepares several quantum systems, denoted by these buckets here, it always prepares them the same way, and the experimenter out here performs measurements on each and every one of the systems, he accumulates statistics, and from the statistics, he recovers some information about what this preparation device was, is. But like I said before, how can that have any sense if you've already rejected the idea that quantum states are not ontic, instead they're epistemic? Does it mean that we have to imagine that there's a little guy inside Preparation of Ice who knows these states and what I'm trying to do is figure out what he knows? So this is a bit of a conundrum from the point of view. How do you explain this idea in informational terms or maybe, let me say, Bayesian terms? Well, luckily we have some guidance from the philosophy of probability. We can go back to papers from the 1930s when the hot topic was what does it mean to be an unknown probability, from a Bayesian point of view. And for this, De Finetti A nice theorem that tried to push that issue to rest. When you take a coin out of your pocket and you flip it many times and someone looks at the statistical data, you get the data and they say, ah, it's really a 75-25 weighted coin, the objectivist about probability would say, I found the true probability, or I found the true probability. The subjectivist would say, no, no, no, you didn't do that at all.

47:30 What you did was you wrote down a prior about all the individual point clips, and then you started conditionalizing on that prior, and then it turned into a certain form. And De Finetti characterized what those priors looked like. So he considered situations like this, where let's say we've got random variable 0, 1, and we've got n copies, potentially n is infinite. And what De Finetti showed was that if we assume that this large prior on n experiments is exchangeable, we can take any two experiments and interchange them, then he was able to show that we can always think, we can always act as if, because of this representation there, we can act as if this large prior is given by a mixture of unknown but true probabilities. And this solves the issue from the subject's point of view. In the quantum mechanical case, we want to do something much like that. Namely, instead of drawing this picture that there is an objective quantum state in each bucket, and then saying that our measurements reveal the unknown quantum state, If an observer or agent starts off with a prior quantum state for many, many buckets, this big row zero, I wrote it big because it's supposed to represent the big system, we'd like to find the conditions under which, after performing measurements, we conditionalize down to a state of independent quantum states for all of the remaining systems. And just like Diffinetti, actually one can prove a representation theorem that says the only condition you need is that if you take the large lot of buckets and assume that the initial quantum state for the whole set of buckets is of such a form that if you interchange any two buckets, the quantum state stays the same, if you make this assumption, then lo and behold, you get a representation theorem that looks just like Diffinetti's.

50:00 Only except it's in quantum language. And if you now perform measurements on individual systems, you will update to something that is a product form. Well, what does this have to do with whether quantum mechanics lives on real Hilbert spaces or complex vector spaces or quaternionic vector spaces or some more exotic structure? And the answer is, nicely enough, the theorem only works If quantum mechanics is written over complex vector space. So if you're wanting a De Finetti theorem to take the place of the unknown state in a tomography situation, it had better be the case that quantum mechanics is written on complex vector spaces rather than real vector spaces. So that's the first result of that playbook. It kind of shows you the kind of games that one can play. Let me quickly go over one more phenomenon and then I'll try to save the best. For last, everyone says entanglement is important, but as like Schrodinger said here, I would not call quantum entanglement one, but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of So you get the feeling that there's this mysterious substance or mysterious essence out in the world called entanglement, and I hope Don Howard's here. Oh, he's not. I think the information theoretic point of view about quantum mechanics dispels that. Let me show you in what way it does. I don't think it is the one characteristic trait of quantum mechanics that enforces its weirdness. And the way to pose that question is to ask why entanglement? Where does it come from? And in particular, when you take two quantum systems, for a more general question, you take two quantum systems and you combine them to think of them as one system, why is it that you use the tensor product rule? Why don't you use some other way of combining Hilbert spaces? You know, you could take the direct sum, you could take Grossman products. There's any number of ways of combining two Hilbert spaces into one Hilbert space, but we're taught that we use a potential product.

52:30 Well, to give you an answer for that, let me remind you of what I think is the most information-irregular flavored derivation of the quantum probability rule. It's a completely different subject, right? It's not about entanglement yet. We're just talking about the probability rule. The probability rule is that if you're given a quantum state and you measure some observable, then the probability of the outcomes is given by taking this observable, diagonalizing it, pulling out the eigenprojectors, and then taking the quantum state, multiplying by an eigenprojector. It's called the Born rule. Why do we use this rule? It's effectively the only rule for calculating probabilities that you could have if you make the following assumptions. That measurements correspond to orthogonal bases, this we're familiar with. But also, that when you ask what is the probability, let's say, for this outcome when you perform this observable, so what I'm doing here is I'm making an orthogonal basis, and if I ask what is the probability of getting this outcome, Gleason said, let us just suppose that the probability of getting this outcome doesn't care about the other elements in the basis. So the probability of getting this outcome is the same if you perform this measurement. Or if you perform that measurement or that measurement to that measurement. So that's Gleason's non-contextuality assumption. And then he showed from that assumption alone, nothing else about continuity, nothing else about differentiability, just nothing else, that the probabilities for the outcomes of such a quantum measurement have to be of the form trace of rho on the projector pi for some quantum state rho. But it didn't make Gleason famous. He was already famous for solving one of Covert's ten problems, I think. But he might ask the question, well, what is really going on when we make measurements of bipartite systems in quantum mechanics? So I've got a system over here, and Alice is holding it in the system over there, and Bob is holding it in one hand, and a beer in the other.

55:00 One of the things that we've learned from quantum information theory is that a really interesting arena for problems is the case where we've got people doing local manipulations on one system, maybe measurements or maybe transformations, local manipulations on another system, and talking to each other over the telephone. So this is often called LOCC, local operations and classical communication. Might it be that entanglement just comes from the general probability rule for situations like this? The answer is actually it does. So if you consider a situation like this, Where we've got an Alice and Bob, two systems in front of them. Alice can perform measurements on her system. Bob can perform measurements on his system. And they ask, what's the general form of a joint probability distribution for the outcomes of the measurements? What's the general form for a probability of getting outcome i over here and j over here? And we make the same assumptions that Gleason makes. Namely, that the probability will only be a function of the projectors and not the whole observable. This is something that Einstein will attack, so this will be fun. Then, lo and behold, look at this. This function, which is defined not on the tensor product, but it's a function defined on the operators, Cartesian products of the operators. This probability rule. If you massage the mathematics, I mean you do some mathematics, you massage that little thing, then just as Gleason showed, you get something very simple, namely that there must exist a linear operator on the tensor product of the two spaces, such that the probability is given by the standard form rule, but again using the tensor product of these two projectors in the expression. Well, not almost nowhere. There isn't a strong assumption of non-contextuality, which has something to do with saying there's probably no hidden variable theory behind it. That's one thing. The other thing is that local communication and local manipulations are built in from the start. There's nothing to do with non-locality, at least as stated, unless somehow non-locality is deeply hidden in the very structure of measurements on a single system.

57:30 So that's another example, and I'm guessing that I've probably run out of time. The only other thing that I would have liked to have told you is what counts as a quantum measurement and why, and can we give some kind of information, theoretic gloss, on that, and I think we'll wait on that. But let me tell you what the overall view is pushing for, and then we can pick back up there later. I think the place to do place to start is to look back at Bayesian probability theory again. The Bayesian would say that probabilities are not real. They're not real in the sense of existing out there independently of the agent. But you ask the Bayesian, must coherence hold? Coherence in the Diffiniti sense. And Bayesian would say, well, that's what you should strive for. So coherence is a normative constraint. An individual agent may not be coherent in any sense, but he should strive for coherence if he doesn't want to lose his money. I think what quantum mechanics represents ultimately is a behavior change for agents, betting agents, gambling agents, who are immersed in this world, the world of particular properties. And what quantum mechanics represents is a normative theory for his actions. Now, to the extent that it's a normative theory, you look at the structure, like coherence, and you say, that tells us something about the particular world that we're in. See, coherence really doesn't, in the usual probabilistic setting, because it's about all possible worlds. But there's something added to coherence, and that gives us quantum mechanics. And that structure, whatever it is, this extra stuff that we add on top of probabilistic coherence, I would say is the zine that makes quantum mechanics fly. Thank you. A few minutes of questions. Christian, do you have a few? I have three minutes. Well, three minutes of questions. Okay. I'll take questions rather than show you the great stuff. Are there any? Yeah.

1:00:00 Well, I can answer the question that, well, I can say that quantum mechanics was indeed But then quantum mechanics is also deeply troubled for the last 75 years. So, you know, you can say that by a hodgepodge of various efforts, and there are a lot of derivations of quantum mechanics from fundamental principles, operational principles, but then people say, that's just not enough, I need more, you know, tell me your operational principles, but I want to know something about the world. And it can be the case that, well, people think that they have operational derivations of quantum mechanics and that they're purely operational, but if you look at them very carefully, you find that there are hidden assumptions about the way the world is. So, yes, you know, I'm sure Schiff developed quantum mechanics in one way. Eugen Merzbacher, that was the book I studied when I was in school, developed it another way. And all of those are satisfactory to some extent, but if the issue is quantum foundations, I think the only marker for progress is that we find something that is so compelling, so beautiful, so unique, so simple, so productive, that we look at this structure, whatever it is, and we say, ah, we're at the end of the road. It's time to drop this question of quantum foundations and quantum interpretation and move on to how we can develop this into something truly fantastic, like let's say when Einstein got his principles and then Minkowski massaged them into space-time, flat space-time, it was time to move on because it was clear that you were at the end of the road and maybe you could do something more if you take that as your starting point. That's all I'm shooting for. Well, let's have another question. There'll be time later on to discuss it. Sorry, that's the end. There's a discussion later. There's a question here. What will the information stuff be? We'll wonder what the answers will be. Oh, it might well. It might well. So, you know, all of this is exploratory. You shouldn't take anything that I ever say, at least, as the final word on anything.

1:02:30 You know, it may be the case that when you write out the formal structure like I did, you're just not able to get an information theoretic reason for anything. And then maybe we go to, let's say, someone else's formal structure for quantum mechanics, and you look at that and you go, bam, this one is information theoretic, this one is, but this one isn't. So one needs to play with all of these and see where they lead. At least in one that I wrote out, I had some yes answers, and then ultimately, if I ever had time to give a five-hour talk. I have some no answers, and it's the no answers that look promising as foretelling us something about reality, but I wanted to put it in such a way that I can show you that progress can be made, that at least with this formal structure you can look at it and say, some of these things are of an information delay. I want to begin by talking about the theorem that Clifton, myself, and Hans Halvorsen came up with, which I'm going to refer to as the CBH theorem, the Clifton-Bruth-Halvorsen theorem. Because my talk is really based on that. Now firstly, I just want to make clear where it came from and the motivation. Actually, the idea was to see if we could come up with the basic outlines of a quantum theory description of physical systems from the assumption that we live in a world in which there are certain constraints. On the acquisition and the representation and communication of information phase, but here, The idea was not to do something that, I think, Wheeler was looking for. It seems to be a bit that somehow the stuff of the world can sort of be reduced to information, that little information office or something, you know, out of which that stuff of the world is made.

1:05:00 Well, this does not say anything like that. I mean, we want to do something that can get the basic outlines of the physical description of the world from certain... Information authority laws of nature, if you like, which would be constraints on the exposition and the representation and the communication of information. Well, the basic idea for that came from a conjecture by Chris and Gilles Bossard. Bossard referred to it as a speculation. He didn't want to go so far as saying it was a conjecture, but the idea was that quantum mechanics could be derived from cryptography. And that actually seemed very exciting. The proposal then was that from two principles of cryptography, the possibility of key distribution, and the impossibility of a graphic protocol called bit commitment. You could actually get quantum mechanics. And that seemed very intriguing. I mean, you've got these two cryptographic principles, which are, in a sense, information theory principles, and the idea was perhaps you could get quantum mechanics from that. Let me just say, key distribution, I guess people know that. I mean, it's the ability to distribute a secret key. This commitment is a little more, I guess, A protocol that only cryptographers maybe know about. Let me just say briefly what it is, but we can sort of forget about it in that sense. Afterwards, a bit-committing protocol is a protocol like this. You've got Alice and Bob. And Alice makes a commitment to a bit. That is, she chooses a zero or a one. And then she sends some information in the form of physical systems to Bob. And the information has to be such, or the physical, the information encoded in the physical systems has to be such that it is what's called concealing, that is, Bob must not be able to, by looking at it, doing any measurements he likes on it, determine what Alice's choice was, 0 or 1.

1:07:30 At a later time, Alice is supposed to send some further information to Bob, in effect a key, and putting the original systems which he's Which he is holding together with this further information, Bob should be able to confirm. All of these are key terms that can be used to define a system. If Alice made the commitment that she did make, in other words, if she makes the commitment on Monday, she just decides, writes it on a piece of paper, just so she doesn't forget it, zero or one, sends some systems to Bob, which may arrive on Wednesday, then the information in those systems should be concealing for Bob, in the sense that we can't tell what the commitment was, and it should also be binding. For Alice, so that she's sort of locked in, she's not supposed to be able to make any changes. On Friday, she tells Bob the commitment, I committed to zero, and then he says, well, prove it, and then she sends him some further information, and with that information, he can maybe do certain measurements on your systems and confirm that was in fact the case. Well, if you can do bit commitment, then you can do all sorts of fancy things, and it turns out that you can't do unconditionally secure bit commitment in classical theory. Unconditionally secure means secure by the laws of physics. Okay, so that was the original idea, and Rob Clifton and I thought about it and played around with it. Later on Hans Halvorsen joined the project, and this is basically what we came up with. The idea came from Rob, because he and Hans have been improving all sorts of terrific things in C-star algebras. I actually knew nothing about C-star algebras. We should start off with the mathematical framework and C-star algebras, which... It's a broad enough framework to include all the theories that have ever been proposed in physics for the last 400 years or so. Broad enough to include classical mechanics, quantum mechanics, field theories, hybrid theories, and so on. And then within that framework, that background mathematical framework, impose certain information theory constraints. And then attempt to show that the constraints cut out all the quantum theories.

1:10:00 And when I use the word quantum theories, I mean a quantum field theory or a particular model of quantum mechanics, maybe referring to systems with discrete observables. That would be a particular version of quantum theory. Okay, so the three constraints we came up with were the impossibility of superluminal information transfer between two systems by performing measurements on one of them, the impossibility of perfectly broadcasting the information in an unknown quantum state, and the impossibility of unconditionally secure bit commitment. It is simply a generalization of the notion of copying or floating, so the second condition could equally well be formulated as the impossibility of perfectly copying. The information contained in an unknown, pure quantum state, and we didn't want to have the conditions for the pure quantum states, and it turns out if you want to just refer to any other state, we need to broaden the notion of cloning or copying to broadcasting. Since it doesn't play a role, you can just think of that as copy, not clone. That these two principles jointly entail, in the framework of C star algebras, that the algebras of observables pertaining to distinct physical systems must commute with each other. That is, the operators in Alice's algebra must commute with the operators in Bob's algebra. It must be non-commutative, which gives you interference, and thirdly that the world must be non-local in the sense that space-like separated systems must at least sometimes occupy entangled states. And those three physical characteristics, at least these, we took to be definitive of what we take to be a quantum theory in the most general sense.

1:12:30 And this is an old slide, I said you also prove the converse except for an open question about non-locality in this movement, but Hans Halvorsen later closed that loophole. So indeed you have a characterization theorem in the sense that these three information theory principles give you these three principles and you can go backwards the other way too. Okay, what I want to do now is demystify a little bit these principles, and because it might just seem, well, they just suck out thin air, you know, there's this no commitment, you know, what really is going on? Well, you could reformulate the principles this way, maybe a little relatable topic. The first principle just says that the state of a system, or if you like, the information available to a system, is unaffected by the occurrence of a measurement on a distinct system. Now, really I think that that particular constraint This should really be considered as part of what one means by a distinct system. Actually, we have in the framework of C star algebras a very weak notion of distinct system, and two systems are distinct just in case for any state of A, any state of B, there's a... A state of the composite system of which the A-state and the B-state are marginals. In effect, that notion just says that Alice can choose any state or create any state independently of Bob's state, which is the idea that, well, they're distinct systems. If they weren't, then there would be some constraint on Bob's side of what could happen at Alice's side. The first constraint says If the measurement is going on in Alice's region of the universe, and by measurement I mean here a non-selective measure, the physical process that has taken place, I mean Alice might have selected the particular outcome, but that information doesn't get transferred to Bob, and in that case there's no change in Bob's part of the universe by the fact that Alice has gotten some apparatuses and there's some kind of measurement interaction going on in there.

1:15:00 Bob's state of the universe remains the same. And that's all I've got to say. The second condition for pure state space that I can talk about copying and cloning and not talk about broadcasting says, really, there's no universal copying machine. Now there is, in principle, a universal copying machine in classical theories or commutative theories. You can show that you can, in principle, have a device which will take any input state and output the input state in a copy. Equivalently, you could say there's no universal measuring device. There's no device which, for any input state, outputs a distinct pointer state or pointer reading which is going to be correlated with the input state. If you have that, then you could just prepare these states. And conversely, you know, if you can't read them, you can't measure them. So this principle really is saying that there are no, there's some constraint relative to classical theories on measuring or on copying. Now, it turns out that from these two constraints, or really just the second one, if you take the first one as part of what you mean by distinct systems in the framework of the C star algebra, it turns out that there exist unambiguous, sorry, ambiguous mixtures in the C star algebra. Just as it is in quantum mechanics. States that can be decomposed non-uniquely into convex combinations of fewer states. And so, and it's that which will make, well, that will also give you entangled states. I mean, from the first two assumptions in a C star algebra you'll get the existence of entangled states. There is a claim that, it's been argued, that the third constraint about no-bit commitment is really redundant.

1:17:30 I mean, if the third constraint is really giving you entangled states, well, you've got them already once you've got the first two principles. To a certain extent, I mean, the charge is correct, but I want to, in the sense in which, you know, we... In the sense of what we claimed in this paper. But I want to say that now that I think the situation is just a little bit different. We can formulate, and I want to argue for keeping all three constraints, the first constraint can really be reformulated as follows. The first two just say something about measurements and quantum mechanics. The second one also says something about measurements and quantum mechanics. Three pair of measurements on a system S that generate different convex combinations of fewer states that are . There exists a state of a system S plus S prime, some other system, This S-prime system, such that the outcomes of the primed and the unprimed measurements are correlated, that actually follows from the first degree. And it's that that thwarts Witt's commitment. And in fact, it's that formulation that's actually used in the proof, effectively. There are a number of things that are required for an open commitment, which doesn't follow from the first two assumptions, and that is that these correlations are preserved under, well I should say, spatio-temporal separation. These correlations are preserved under spatio-temporal separation, and it's prime in terms of how that works out, and the aim of this part of the discussion is to try and make those Three constraints in natural, because just sort of talking about no bid commitment and no cloning, you know, what are the constraints? So here's what the third constraint amounts to.

1:20:00 If you have a source which is producing a correlated state, an entangled state, that state psi there, which is the singlet state of the usual Einstein-Kodolsky-Rosen state, then the reduced state on Bob's side is just half the NN. Half the identity could also be represented equivalently as a mixture of 50% plus and 50% minus, or equivalently as 25% state phi 1, 25% state phi 2, and so on, where phi 1 and phi 2, phi 3, phi 4 are four non-orthogonal states, four non-orthogonal states in the two-dimensional system. You can just take those states and write down the density matrix and post those and you'll see this copy I did. What Schrödinger pointed out was that in a two-part paper in 1935 and 1936 that he wrote on the EPR paper, a very profound two-part paper on the significance of the EPR result, And he used the word steering and effectively steer Bob's particle into any mixture compatible with the density operator by appropriate local measurement that is on Alice's side, possibly involving what is now called an ancilla particle. So Alice can take a particle in an appropriate state, perform a measurement on the combined green and red particles. And she's going to get, I mean the measurement will have to have four possible outcomes. So that little red or orange particle is also going to be a two-dimensional system, and the green and orange system are going to be four-dimensional, so she'll perform a measurement of four possible outcomes, and she can choose the situation such that the four possible outcomes are correlated, that the outcomes are probabilistic for Alice, so she can't literally steer Bob's system into the state by one. But what you can do is you can perform a measurement on the base of which you get one of four possible outcomes with certain probabilities. And depending on which outcome, she will then be able to say, Bob, hey, Bob, your system is in the state phi 1, and check it out and see it. If he does, then he'll check it out.

1:22:30 So it's in that sense that Alice can steer Bob's system into the states phi i or certainly the states plus or minus. The states plus or minus, she just performs a plus-minus measurement on the green system. Okay. Well, this is really the basis for teleportation, because here again is the same situation represented as a teleportation scheme. Alice, as one says, is given a particle in an unknown state phi1, phi1 being the same state that I have on the previous slide. And then the composite state is the product state of Psi 1 and Psi, the entangled state, Bob's reduced density matrix is that density matrix, which is half the identity, and now Alice performs a measurement of... Of an observable state with eigenstates being one of the four simple Bell states, 1, 2, 3, 4, and depending on whether she gets 1, 2, 3, or 4, she will be able to tell Bob that the state on his side is some unitary transformation of phi 1. Thank you for your attention. The possibility of this Schrodinger steering, which is really the possibility of teleportation, is really what the third construct is saying is possible. Combined combinations of physics, blah, blah, blah. That system ask would be...

1:25:00 Bob's system, so what I call in the other slide Bob's, and the two measurements, M1 and M2, would be the, you know, associated with those different deep entity. And there exists a system S plus S prime. S prime is Alice's system plus the ancilla, if there is an ancilla. And some, depending on what you do, you may or may not need an ancilla. All of these terms are related to a particular type of measurement, which is called Poisson's method, or Poisson's method, or Poisson's method, or Poisson's method, or Poisson's method, or Poisson's method, All of these are responsible for the impossibility of good commitment. Because Alice can do that, I won't go into all of it, the theme of this little discussion was to make those axioms seem... It seems somewhat natural in being associated with, in the case of the second axiom, interference, and the third axiom, entanglement, because it's entanglement that enables you to do teleportation, it's entanglement that enables Alice to steer Bob's system in a certain way, and it's also... Entanglement, which is really associated with, by a few states, with compendium of space. So this seems like a natural way to get at what is essentially quantum mechanics. But this leaves open, well, you know, the question that worried these two guys. What does it all mean? So we've got a characterization theorem and four quantum mechanics in terms of assumptions about measurements and measurement and information.

1:27:30 And by information throughout, I'm thinking of information in the Shannon sense, appropriately generalized to a non-commutative situation. And so, but maybe this will come up later, it seems to me that these questions about whose information, what's information, are really beside the point. I mean, for Shannon, information is associated with some source that is producing probabilities of producing events with some... Key terms include probability distribution and rich-handed information associated with that. If you want to know whose information, well, that's sort of irrelevant. You've got this physical system here which is producing these signals and you can associate an amount of information. And you can associate notions of compression and so on with that amount of information. And if you want to know what information, well, you know, it's whatever that is going to be, those signals. One of the sources that you see is that distinguishable events are correlated with. So if this urn is sitting over here and according to my physical description it can take one of two positions, then I can say that in principle this can encode one bit of information. And if you ask me what is the information about, well it's whatever the direction of the urn is correlated with. That's what it's about. And this seems to me to have nothing whatsoever to do with the fact that there's a correlation, the fact that there are two possible states here, and it seems to have nothing to do with, you know, whose information, you know, what's in the cloud. The cloud is the correlation, and whose is irrelevant. But still, you know, what about the measurement problem? What about, you know, what is all this information? What does the characterization theory say about the puzzles that we sort of know and love, so to speak? Well, I, the Clifton-Boole-Hollison paper didn't really say much, if anything, about that. Really, on purpose, because when Hans and I wrote up the paper, Rob was no longer with us, and we wanted to, well, we didn't want to sort of go out on a limb, because the paper was a three-man paper. We didn't want to go further than just the basic mathematical result.

1:30:00 But I subsequently did sort of stick my neck out with a paper called Why the Quantum, and I argued for three theses. And the first was that quantum theories are relatively innocuous. I mean, this we did say in the paper, that given the characterization theorem, quantum theories best understood... As a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of non-classical waves and particles, and by information and the information in the Shannon sense. Okay, so the second claim is kind of, or requires a lot of argument, and that is, I said, given the information theory constraints, any mechanical theory of quantum phenomena That includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory. Now, well, maybe I'll just go to the third one and talk about this. And then the third claim was that assuming that the information theory constraints do in fact apply, are in fact satisfied in our world, then no mechanical theory of quantum phenomena that includes an account of the measuring instruments, or includes an account of measurement interactions, can be acceptable. And the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information. So now these are very strong claims and... Actually, I'd like to just sort of stop there, but I should say something about where they come from. So, I don't want to go through the whole paper, why the quantum, but just how much time do I have left? Um, you've got 10 minutes and 15 minutes. But I want to say that the argument for the second and third theses were in something like this. Look, uh... If you're starting off with a C-star algebra as, in effect, sort of constitutive of what you mean by a physical system and what you mean by observable and so on, in terms of very, you just want a kind of an algebraic structure that has enough structure so that you can talk about these notions in a minimal sense.

1:32:30 Then the way you want you to think about that is as follows. You talk about observables, you talk about states, which have an algebraic structure. So the underlying assumption, the background assumption is that we just have measuring instruments which are associated with these observables. Should be thought of just as black boxes at the start of the investigation. That is, they come from some previous theory that we're now using these black boxes to move to a later theory. So, from the point of view of the later theory, they're just black boxes which are producing outcomes with certain probabilities. And then we find out by using, and think of these black boxes as like David Albert's, you know, color boxes and hardness boxes in his book on quantum mechanics, they're just boxes which produce two outcomes and you get certain statistics by going out in the world and using these boxes. Then you gather some data and you take a look at the data and you formulate these three constraints because they seem to be characteristic of the data and then you get quantum mechanics, then you get your undersea star algebra and so you exclude the commutative algebras and you live with the non-commutative algebras, the non-commutative algebras which have entangled states which are robust. In a certain sense, that is, you know, as the systems move apart spatiotemporally, they remain there, and so your key styles are of that sort. Now, you ask the question... Does there exist a phase-based representation of the C-star algebra, because it would be nice if you could have that, because then you could replace the whole machinery of C-star algebras with a phase-based theory in which you could talk about points as bicycle states and your observables in the C-star algebra would then be replaced by dynamical quantities in your phase-based theory.

1:35:00 And you wouldn't have any further interpretative problems. Well, it turns out that you don't have that representation theorem. There's no face-to-face representation. And so now you have to ask, well, how do I interpret these states which are expectation-valued functions over observables and so on. Okay, I then argued, and that is sort of the second and third one, Thank you. Given the fact that there's no face-based representation, you now want to look at some kind of extensions of quantum mechanics in terms of invariables and so on and see whether you can go back to a sort of classical life view of things, because it's a view of a situation. And I then argued that given the three constraints, any such extension of quantum theory must be empirically equivalent to quantum mechanics. And I argued, and of course we can talk about this a little later, that on the basis of an undetermination argument, which I think is a little different than the usual undetermination argument, but I'll just leave that hanging for a moment, I argued that... There would be no grounds for believing any of the extensions of quantum theory, and I, in the paper, made a comparison between Bohm's theory, a sort of invidious comparison between Bohm's theory and Lorentz's theory relative to relativity and quantum mechanics, and showed how Boehm's theory would have to, if the information theory constraints hold, Boehm's theory has to include some assumption within the variables that reach their equilibrium, and then there's going to be no evidence available to get this. But I also argued that given that these information theory constraints are now understood as information theory laws of nature, this is sort of an in-principle All kinds of kinds of dissemination and that would be grounds for withholding belief in these theories. But it seems to me now that maybe that's a little... Oh, and then I should say, okay, so then what about Einstein versus Bohr? Well then it follows that measuring instruments, the ultimate measuring instrument, is always going to be...

1:37:30 All of these are outside the theory, a black box. I mean, you're going to be stuck with your C-Style Debris formulation. And while that doesn't mean that there's sort of a class of systems which are black boxes, it means that in any application of this theory, there's going to always have to be some ultimate aspect of whatever you take your measuring instrument to be, which is left outside the description. And you can always then put it in the description, but something else is in the outside, and so you don't escape from this formulation. And it's in that sense that there's no measurement problem, because there's no measurement problem because of, in effect, for the same reason the board book, there was no measurement problem. There's a, you know, the inner sense of the measuring instrument is a black box. There's a further measurement problem, which is why in this, given the fact that you have a noncommutative C-style algebra and so on, which is describing the world we're in, I mean, where do you get the classical world from? And that question, I think, has to be answered by decoherence. So that basically was the condition in which it was. Now, it seems to me, I'm just going to, I'll say just a little bit about this, and perhaps, you know, come up with a reason. It seems to me that there's another way to go here, and because this whole position that I've argued for has sort of been challenged as well as another form of instrumentalism by various people, Simpson for one, and various... Students that I see here, like Michael Safone and Dan Parker in my seminar of being a semester on the subject, and I mean they sort of accuse me of being basically a closet instrumentalist, so I've been trying something else out which I'm sort of hesitant to sort of talk about here because I'm not sure whether it makes sense, but basically the idea is this. I want to use two moves, if you like, that I've come up in different... Oh, I should mention Ivan Silvestri, too, who's in the back there, who comes along to my seminar, and who's also challenged me in this respect.

1:40:00 This whole T-Style Debris framework also fits very nicely with the relational interpretation of quantum mechanics. It's not going to change much, but it's going to change a bit. And the relational interpretation that I have in mind is an interpretation that's being proposed by Collar and Bailey. The paper is called Relational Quantum Mechanics, I think, and maybe some other papers as well. I want to refer this analysis to that paper, or use that paper as sort of an underlying point of view, use that position as an underlying point of view. And what that buys me is the following. It seems to me that I can then... Exploit a principle that is exploited by David Wallace and Simon Saunders in their Everadian interpretation of quantum mechanics. A principle which gives them that the probabilities are rational bending probabilities. If you think of a basic interpreter problem as something like this, look, you've got the three information theory constraints, and they tell you that there's no face-based representation on this quantum C-style. The fundamental question then is, well, what do these probabilities mean? I mean, putting it in terms of a simple two-dimensional Hilbert space, how do you understand these quantum weights, if you like, which are associated with different bases? The weights are associated with the angle. So you want to say, well, these angles represent probability. They're not representable in the usual way because you don't have a face-based representation. So how do we understand these weights? Well, in the average interpretation of Wallace and Saunders, you prove on the basis of a decision theory document.

1:42:30 That the weights represent rational betting probabilities. And the essential thing that gets you that argument is a principle that Wallace calls equivalence, which amounts to saying there's no fact of the matter about the outcome of a measurement. And there's no fact of the matter about the outcome of the measurement in a many worlds interpretation because, well, you know, all outcomes occur relevant to different worlds. It seems to me that you can also have that principle in a certain different sense, but something which has played the same role in a relational interpretation. And so if you couple this with a relational interpretation, then you can then say, well, these probabilities are just rational varying probabilities. I think that that might go some way towards disarming the accusations that this is just another form of instrumentalism. Okay, so I'll stop there. Thank you. Can we break for a few minutes? Probably. So it seems that you have accomplished what the first speaker, Chris Fuchs, was saying, that you have come up with an inferior principle for quantum mechanics, right, so you have these two possibles, but of course, you know, like, so then Chris pointed out that you have the next step, so you're going to develop, like, a constructive theory. You told us a little bit about that as well, right, saying, like, of course, with relativity, you have the alternative, which is that being a Lorentzian, and that is your constructive theory. You're saying now that a lot of the interpretations on the table for quantum mechanics or boolean mechanics, modal interpretations now look a lot like Lorentzian view. From this standpoint, right, the nearby become like extremely unattractive. So what I don't see is that what you're not, what you're left with is not simply that you now have to follow sort of the, if you want to go constructive, right, the sort of a no-collapse ever-ending sort of portion. You have more, and I guess like a, that was the sort of thing you were talking about like at the very end of your talk.

1:45:00 So I want to hear more about why it is that you resist that. Well, okay. In the paper, Why the Quantum, I actually argued as follows. I argued that quantum mechanics is a principle theory, a principle theory of information. In the same sense in which relativity was run by Einstein as a principle theory and made the distinction, as he was brought out, between principle and constructive theory. And then I wanted to argue... This seems to me at one time as a crucial insight that quantum mechanics is a principle theory for which there exists no constructive theory, sort of quote-unquote, but obviously there do exist constructive theories, Bob's theory, the constructive theory, and so on, so it can't just be that there don't exist constructive theories, so I tried to replace that for which there exists no constructive theory. For which there exists no constructive theory, by the argument for which there exists no acceptable constructive theory, which is sort of the methodological argument. And this was resisted by some people, anyway. So what I'm now proposing is... To say that, well, the constructive theory has to be a quantum theory, and I'm proposing not an Everettian theory, because that doesn't seem to fit with this in a particularly rational way, but a relational theory. If you go back to my original way of looking at things, you've got a C star algebra, you think of the measuring instance as black boxes and so on, then you try to prove a representation theorem, see whether you can replace all the story by a face-based theory, while you can't, so you take the view that... Really what's going on here is that quantum mechanics, there's no detached observer view for quantum mechanics. Well, there are different ways of spelling that out. One way is to say what I wanted to say before, which is that the measuring instrument is ultimately a black box and there's no detached observer.

1:47:30 But our relational view, there's also no detached observer description. You just have, you know, a different physical title if you like, descriptions. And so this seems to fit very well with the C-style algebraic formulation. And so... I mean, the answer to your question is, it's not that I'm proposing an Iberian picture where there's one universal wave function and that's sort of the reality, but rather that there are a bunch of systems which are characterized in terms of the C-style of the brain framework, and the states are just relative states. And the values are just also, the values of observables are also just relative values. Now, I mean, there are lots of questions you can ask about that, and because, I mean, there's some subtlety associated with that. So, at the moment, all I've said is, you know, it's what Rovelli says, you know, but that's not, that raises a bunch of questions. I guess I was a little bit worried about the degree to which you wanted to refer to these. One thing I have in mind is the following. One thing I have to know about these black boxes is, well, two things I have to know about them. One is that they're not just randomly spinning out numbers and understanding what should have been fruitless. I have to know that two of them are actually somehow doing the same thing because I don't collect all my data. So, we know those things in fact. Well, we know them because we have a theory about how they work, what they're actually doing. And that theory actually largely is quantum mechanics, at least in the broad sense of the theory that we call quantum mechanics, used by physicists. So somehow it doesn't seem, when you put that fact into the mix, it doesn't seem so external anymore. It's not just this sort of separable thing. There's quantum mechanics down the path, there's information theory I can understand it better in terms of... Thank you for your time, and I look forward to working with you again in the future.

1:50:00 In any particular application of a theory, the application of a theory has to be relative to something which is doing or looking or measuring or assigning of values and so on, and that that thing itself is not... This is not being included in the description in the same way that it would be in a classical description. And that, I think, is what you do get in that interview. You could say, well, that means it's always from the perspective of some system that you're doing, that you're assigning values or that you're assuring the probabilities to that system, and you're not describing that system as interacting with the other systems in the same way as you do classically. Well, whatever bit you left out, you can always, from a further perspective, describe the interaction as an entanglement, but then it's always from some other perspective, so there's always something, there's always this sort of perspectival aspect which is inherent in the non-commutativity. So maybe what you meant to say is something like, it's not an external theory somehow, it's rather, it's rather the theory applied in some other perspective. You can give me the theory of the block, but the so-called black block. Is that fair? That's clear. At that point we should probably throw this section to a close. Thank Jeff again, quickly. It's great for, say, two or three minutes before we come back to hear Anthony's alternative view questions.

1:52:30 I didn't have any exceptions on what you were saying, so it's probably true. That's enough to go. You look like you didn't have any objections. Not at all. And I would, like almost every view graph that you have, I could write another view graph for a class like this. More or less, what you were saying is our approach. I think it would be worthwhile. I have an hour of course, we have 50 minutes. Definitely, rules left or left for your academic bureau, just as quickly as possible. And, of course, you don't have that rule by default because you limit yourself really too much, which is narrower than the approach. Why don't you hear? Also, I have a little bit of a question. I just want to make sense of the interpretation of the algebra. But the algebra itself is, of course, much broader, and the algebra itself has states, of course. But those are the states which don't have the labels. I have lots of things to say, and I also know very much why the confusion between the states in terms of psi and others, when the states of the system itself comes about, because that is the very peculiar feature of it. I have a question. Jeff's position is really confusing because he starts with the C-star level and whenever it comes to details, he immediately switches into a little bit of a stretcher of presentation, so you never know what he's talking about. He doesn't use the room which he conceptually would have to make something with it. To be more honest, you could just say, yeah, I can do a special presentation, and here I go. This one. I certainly don't think he's funny enough. That's too much. I also have prejudices about probability. I think that's probably one point where you and I get a good explanation here. It's quite crucial for this approach. Nothing I said today, though. I think you're right. The parts I'm presenting in public, we're quite overlapping, and the devil is in the details about how crucial it is that one chooses position and probability. Is it crucial or is it not?

1:55:00 Right. So I was going to say, on the optics part, we agree. On the subject, subject, subject is part of it. Or we might have translations. We might have translations. You know, and the reason why all this measurement discussion which we had last night, we have kind of complex state of things, because the reason for that is that you want to go from an objective to a dictation approach. It's not because you want to have an objective to a dictation. It's because you want to go to an objective one, and that's what keeps you from doing it. I don't think that's true. What I think leads me to stop is, it just says, you've got to cross the code distribution and here's a compact way of expressing it. You've got to go to an objective, but there's a picture of the focus. I don't understand what you mean by objective, right? Does the just-standard way of talking about this talk about this? The result of the quantum, the result of applying the quantum, I still think of that as a subjective basis, expectation, and in fact, much like the puck I gave you earlier, there I just try to get rid of. So, thank you for the opportunity. What I'm trying to do is interpret pure space as part of the process because in a certain formulation of the position of quantum mechanics, I mean that kind of quantum mechanics, in that formulation, the space-space is one-two as a one-to-one metric into the three dual... The other three are papers, and those are the ones that I'm going to talk about today.

1:57:30 And you have the pre-rule of the representative of the two worlds, and I think the non-representative of those worlds. One can correspond to the other. I think it's hard to use the characters at all. It's a convincing experience because I've seen too many things. I've seen too many things. I've seen too many things. I've seen too many things. I've seen too many things. I've seen too many things. I've seen too many things. I've seen too many things. Okay, yeah, but what do you, you know, you've got great work on here. No, sorry, let's start at the top here. Yeah, okay. Thank you for your attention. Thank you for your attention. Again, I don't know whether you are Russ, I don't know if I spoke some more than one minute. Yeah, what do you want to speak more about? I don't know if I spoke more than one minute. Yeah, that's right. I don't know if I spoke more than one minute. I don't know if I spoke more than one minute. I don't know if I spoke more than one minute. Thank you for your attention. Thank you for your attention. Okay people, I feel as though I'm ready to make a start to the continuing this morning's session, and Anthony's going to present to you a rather big perspective on things, on this quantum information issue.

2:00:00 So, following Anthony's talk, there'll be time for a round table discussion and hopefully we'll crush out some of the interesting points that have come up so far. So if you want to fire away, Anthony. Okay. So, you just quickly give you an idea of the structure of this talk. I've had too many things I want to say in a short time, but... The first thing I wanted to point out is a criticism of Einstein's 1905 approach to special relativity, which seems to me to be kind of operationalism in physics that treats equipment as something that is regularly self-sufficient, as Einstein put it much later. I'd say something about non-equilibrium hidden variables and a possible realist view of quantum physics. And then with that background, which I hope to get through the background quickly, so I'll have time to give a critique of Clifton, Boo, and Halverson's point of view, and if I have time also, Hardy's axiomatic formulation briefly, though perhaps I'll leave that to the end in case I don't have time. I'll talk a little bit about a comparison. With thermodynamics, and then critique some arguments that have been given by Fuchs and some of his co-workers. So, first of all, let me just say something about the measurement problem. I'd like to quote something from John Bell, who said in an interview with Paul Davies and Brown, So the problem of measurement and the observer is the problem of where the measurement begins and ends, and where the observer begins and ends.

2:02:30 When you analyze this language that physics is about the results of observations, you find that nothing very clear is being said. And what I'd like to ask first is how did physicists fall into this way of speaking? And just as a side remark, The measurement problem is quite often presented in the form of, well, there's a problem with superposition states, but of course it might be that the state vector for pure states is just a statistical object, as Einstein thought, as Ballantyne argued strenuously in the 70s. And that might be true. Perhaps science is just statistical. From my point of view of hidden variables theories, I tend to use Breuil-Bohm theory a lot as a concrete example of hidden variables theory, like not BV theory. In that theory, there is an ontological wave function. But there is a candidate, Nelson has a stochastic hidden variables theory that claims to be based on a sort of Brownian motion processing configuration space and from this the wave function is supposed to emerge just as a mathematical entity describing the probability distribution configuration. I'm not sure Nelson's theory is actually consistent. There's an objection to it by Wallstrom in the 90s. I won't go into that. I just want to mention that there are, of course, interesting arguments for the reality of pure states, arguments to do with Bigman's friend and so on. These seem to me interesting arguments, but I'm not sure how conclusive they are, so I'm just not sure about this particular point. But the point I want to make now is that, again, how does this fall into this language? I'm going to point to Einstein 1905 in which you see, here is Einstein in 1949 criticizing his earlier self in 1905. In his autobiographical notes, he's talking about special relativity, and, of course, special relativity starts out with some primitive notion of rods and clocks and light beams, and you come up with what you see as a sort of operational definition of simultaneity and so on.

2:05:00 So Einstein says the theory introduces two kinds of physical things. i.e. measuring rods and clocks and all other things, for example, the electromagnetic field, material point, etc. This, in a certain sense, is inconsistent. This is my emphasis. This, in a certain sense, is inconsistent because, strictly speaking, measuring rods and clocks would have to be represented as solutions of the basic equations. Objects consisting of moving atomic configurations, not, as it were, as theoretically self-sufficient entities. So it seems to me that what Einstein is pointing to here is that the 1905 paper, there's a confusion between phenomenology and fundamentals. Okay, a fundamental, well, let me go on. So a fundamental theory, oh, no, I'll come to that later. I'm trying to go quickly through this background. Okay. And it seems to me that this is the sort, this 1905 paper, is the source of this attitude that was...