Teleportation & Quantum Information

0:00 Today is 12 for the entire group. Our next speaker now is Chris Timson from the University of Leeds. What does this teleportation tell us about the nature of quantum information? Thank you. I'd like to thank the organisers of information to come and speak today. So I'm going to be asking the question of what teleportation tells us about the nature of quantum information. And the answer is going to be not what one might expect. Now, teleportation is familiar as the most interesting phenomena that quantum information theory has revealed to us. Quantum information theory itself brings down to the idea that the behaviour of quantum systems, rather than being a perennial source of worry, which is many of us, might also be a source of opportunity, in particular a source of opportunity for performing certain computational and communicational tasks rather better than one can manage practically, the task can't manage at all, basically. So, familiar examples, given the existence of Shor's algorithm, we know that quantum computers can be exponentially more powerful at factoring algorithms than factoring prime numbers in the best-known classical algorithms. And the sort of case we're going to be looking at today, entanglement, frustratingly, and the distinctive quantum mechanical property can be seen as a very useful communication resource. And that's precisely what occurs in teleportation. Here we have perhaps the most striking example of using entanglement to assist one in a communication task. So here's a little story of the protocol. I take it that this will be familiar to everyone. So we've been given a two-party as Alice and Bob, who share some entanglement state of the two-party. Say it's a singular state for familiarity. And Alice is presented with a system in some unknown quantum state, I, and she wants to transmit this to Bob. But it turns out that if she performs a tube of joint measurement on her half of the entangled pair and the system in a few states she's trying to transmit, then BAM! The fourth side, her system jumps into the state CHI. The systems on her side end up completely scrambled. So this looks like teleportation because the information characterising the state on her side seems to have disappeared from her side and reappeared on the far side with nothing of any relation to the identity of the other end state crossing the space between them.

2:30 So, given its striking and seemingly non-classical nature, we feel that teleportation could perhaps shed some light on the nature of quantum information. What is this stuff, quantum information? How does it behave? And that sort of thing is an interesting question. Well, it's an interesting question in and of itself. What's the nature of quantum information? But it might help us get to grips with some of the more teasing, tantalizing, philosophical issues that the advent of quantum information theory presents this bit. For example, many people take it that development of quantum information theory is pointed to a new way in physics, a way in which the traditional pursuit of understanding the material world should be replaced and take information to be a fundamental building block. So I call this sort of view informational immaterialism. Perhaps the suggestion is, talking to some people, that with this new fundamental theory of information, we should conceive and physical theory being about information in material rather than in material physical objects. It also might help us with this baffling claim that was often made in the literature that information is physical. What do we need to make of that claim? How do we understand the nature of quantum information? We'll be clearer on that. And finally, if we're clear on the nature of quantum information, that might help us assess whether or not use of the notion of information is going to help us when we address our favourite problem, the measurement problem. But unfortunately, there's no consensus on what teleportation tells us about the nature of quantum information. So here are some of the sort of things that people say when they say, well, what does teleportation tell us? Well, some people say, well, you know, it tells us that quantum information may travel in a non-local fashion. Others say, no, no, no, non-local information travel out of nonsense. what we have to learn is the quantum information the new sort of information may travel backwards in time others, a lot more prosaically, say okay, now I don't buy that either it always travels spatially continuously, it can be hidden perhaps legally and excessively in a classical system we'll flesh these options out a little bit later on which one should we adopt, which one's the right way what is teleportation actually telling us my answer is that it's not really fishy about all of them. This controversy, this fishiness, arises from what I take to

5:00 be a very familiar philosophical era. That's familiar as philosophers, anyway. So this is what we sometimes call the era of hypostatization, or taking something abstract to be something concrete, to be something living in the world. And the problem term in this situation is is the term information. What I think drives the controversy and leaves us with this confusing array of problems in teleportation is when we take information to denote something in the world. But I claim information is an abstract noun, hence it doesn't stand for anything in the world. When we recognize that, we can defuse the controversy. The sort of warning that's familiar amongst philosophers here, how Carl Strawson created in 1950, his concern was the concept of truth, concept of information standing in there right on the stairs. So he says that to suppose that whenever we use a singular substantive, we are, or ought to be using it to refer to something, is an ancient, but no longer a respectable error. So that's, I suggest, the error that we attempted into when we think about teleportation. And so to slightly anticipate my conclusion, my thought about what teleportation tells us about the nature of quantum information is that we need to pay careful attention That's what we need to learn. OK, so here's the outline of the rest of the talk. We're going to go a little bit into more detail about puzzles and teleportation, or some concrete proposals that have been put forward by Yost and Penrose on the one hand, and a very different type of analysis given by Doge and Hayden on the other. Once we've looked at those, I want to move on to what I take to be the correct approach to dissolve the conceptual problem that we seem to be presented with. As I've indicated, I'm going to be appealing to the fact Now, that may not be immediately obvious to everyone, so I'll give you a little argument about why information, in the technical sense, even with Shannon and the constant theory of information, is in fact an abstract now. With this clarification in place, we can then consider what the legitimate questions to ask about teleportation are, and these turn out to be exceedingly simple. It's very straightforward answers. good, so here's the protocol in a little bit more detail of course, a percentage of the teleportation protocol just now a little bit loosely, it's not quite like science fiction it can sometimes sound like so, you know, one obvious difference is that in Star Trek type

7:30 teleportation, we make some matter disappear and it reappears over here that's not what we're doing in this case, we're just making a quantum state for this system we transfer to this system, with nothing travelling between them at least nothing that depends on the identity of that constant state. So here's a sort of a sideways space-time diagram of what the protocol looks like. We have two parties, Alice and Bob, and we create some entangled state, which is then shared between time and the state. Alice then performs a measurement in the bell basis, and I'll give her one of four outcomes. Once you perform that measurement, Bob's system will jump into some state identity of the state chi. It's not identical to chi in general. There will be some fixed unitary rotation away from chi. So all Alice needs to do is to tell Bob what outcome of her mission she got. She's to send him two bits. Then he'll know what unitary he needs to perform to come back to make sure he has the state chi. All the way through, nobody knows what the state chi is, but they know that if they perform this protocol as described, then Bob's system, whatever state it's in, will be in the same state as Alice's incoming system. So this protocol, the state kind of clearing a problem system, that's not instantaneous in fact, we actually need to send some classical information to these two classical bits recording out from a bell basis measurement. But importantly, these two bits sent are quite independent of the identity of the state analysis kind of teleport. Now, okay, so it's not quite a science fiction dream we hope so, but it still has some very striking features of a sort of communication do is send an unknown state from Alice to Bob. And we can see that what we've done is striking, and we consider the other ways in which that might be achieved. How else could we do this? Well, in fact, only by sending a system in the state to Bob directly, or more precisely, sending some system that's very closely related to the state to Bob directly. Because, as we all know, you can't learn a state in an individual quantum system, so it would be impossible to learn what that state is and send a description to Bob instead. So we've somehow managed to get the state transmitted from Alice to Bob without sending some system in that state to Bob, nor by sending some description of it. Now suppose that possibly we somehow had managed to learn the state of Alice's system and had sent the description to Bob.

10:00 but in that case, systems encoding that description would have to be transported between Alice and Bob and again, that's not what happens in the case of teleportation nothing that bears any identity to the relation of the state goes to A and B furthermore, if we were trying to send such a description we would in general require a very great deal of information so typically if we're sending the state to a qubit we need to specify two continuous parameters to specify that that's actually an infinitely large amount of information So, telepopulation is really remarkable, because we've done something which amounts to sort of doing this, but in a way that isn't any of them. We're left with a picture which has been transmission of something that's inaccessible with the classical information. We're going to have to call this the transmission of quantum information. In the transmission, the information has been disembodied. It doesn't track clearly the way to be. And this transmission has been extremely efficient. We've only used two classical bills. So this presents us with the two central questions. How is so much information transmitted in a protocol? And just how does it get from Alice to Bob? And it's really the second one I want to focus on. That's the really mysterious one. How does this work? So we're talking about various proposals that have been given now. Okay, so this is a program that's been by Richard Yosa and Roger Penrose. So they concentrate on the issue of where's the channel that this information is traveling down? So instead, the two bits, then, that can't be the channel, they're independent of the state, so they can't carry the information about its identity. So what else is there? Well, it's only the entangled pair, so that must be the channel. So at this point, you could say, well, okay, look, the entangled pair is a channel, and the information flies non-locally from A to B, while it's an entangled channel. But you're also in Penrose demure, so you say, no, no, information can't behave like that. It doesn't make sense to talk about non-local jumping around in information. have to try the space to attend group continuously. Well, what options does that leave us with? Well, Henry has described this rather nicely. How is it that the continuous information of the spin direction per se that she, Alice, wishes to transmit, can be transmitted to Bob when she actually sends him only two bits of discrete information? The only other link between Alice and Bob is the quantum link that the entangled pair provides. In space-time terms, this link extends back into the past from Alice pair is produced, and then it extends forward into the future to the event where Bok performs

12:30 his operation. Only discrete classical information passes from Alice to Bok, so the complex number ratio which determines its specific state being teleported must be transmitted by the quantum link. The link has a channel which proceeds into the past from Alice to the source of the EPR pair, in addition to the remaining channel which regards proceeding into the future in the normal way from EPR source to Bok. There's no other physical connection. So if we're doing these guys, we make the discovery that teleportation shows us that quantum information is a re-branicking new type of thing, a type of information that can travel backwards in time. Well, bizarre. Don't you hate and say, well, that's just too bizarre. I don't buy that information can travel backwards in time. In fact, they argue that information can be seen to travel in a situation in a pretty continuous amount, without having to travel backwards in time between Alice and Bob, how are they going to manage that? In order to achieve this end, they say what we need to do is reinvestigate the role of the two bits that were sent from Alice to Bob after she performed her motion. What we're going to need in this reinvestigation is a fully quantum treatment of the teleportation procedure. So we move to a sort of review in which unitry quantum mechanics is the session. No collapse. And we're going to treat the two classical bits as just the two qubits in which we write the outcome. Homalysis measurement in the computational basis, noughton 1, and as Roberto was telling us earlier today, we just have the noughton 1 states that's effectively like having a classical informational state. Okay, so we start with treating it fully quantum mechanically. And we also make the move from the Schrodinger picture to the Heisenberg picture. This turns out that trigonometry would be quite important. And the way they do this is actually quite cute. I don't have time to go into the details here. But essentially what they do is they consider for each system, they pick a well-chosen set of operators associated with that system, which determine all the physical properties of that system. Effectively what you do is you choose some set of operators which span the space of operators on that system. And so for each of your subsystems, they treat the general picture as having a network of qubits. So for each subsystem, we pick out this preferred set of operators associated with each one. They call those things, that set of operators associated with each system, the descriptor of that system.

15:00 Now of course, as we heard quite a bit about yesterday, if you have a set of operators that span the space of operators on one subsystem and on another subsystem, Take those together, you're going to get a set of operators which span the spatial operators in the joint system. So that means that from the descriptor of system A and system B, we can have those characterised physical properties of A completely complete with B completely. Take those things together to state products of them. That entity, that mathematical entity, product to your operators, is going to completely track the physical properties of the joint system. And that's quite a fun thing to note. And then we say even more about time evolution, of course, Heisenberg, time evolution, and the operators are in this state. We just know that the time evolution of a product of operations is equal to the product of the time involved individual operations. And we say that all we need to do to track the evolution of the entire global state of the system is to track the time evolution of each individual descriptor of the subsystem. Those things determine the global state and the local states, and beat it. Finally, we say, well, actually, we still need the vector state, two, in order to calculate expectation values. Given the descriptor of each subsystem, just take expectation value, and that will determine all the physically observable properties on that particular system. But of course, in the high-level picture, the global quantum state is just fixed. And in particular, for collection, Hayden, it's going to be fixed irrespective of the property of the system. Anyway, that was very quick. I don't need to worry too much about the detail that we've talked about in the discussion. Once we do that, it turns out we suddenly have a radically different picture of what happens in the teleportation. In fact, what we see is that although the two message cubits, the Calvin and Alistair Bob, have no locally observable dependence unknown quantum state that came in on Alice's side. Nonetheless, their descriptors will actually depend on the identity of that state. So it's between message qubits that carry the information from Alice and Bob, in a specific continuous way. But that information is notably inaccessible. You can't see it by looking just at the qubits individually. We need to do some great big joint measurement on the optical system. So, just quickly, here's what a 3D quantum treatment This is the analysis side, this is Paul's side. Start off in a computational basis of neatness.

17:30 Create an entangled pair. Here we do it by having the Hadamard that controls the load. That creates, in this case, the five parts of that. Share the entangled pair between Alice and Bob. System 1 is the system whose unknown state we want to teleport to Bob. So what we do is take the starting state, perform some rotation, and end up with the unknown state, Chi. That is the performance of valve-based instrument by doing this operation here. And right, using these two controlled lock gates, the output of this valve-based instrument of which of the four fossils that happens to observe onto these two message qubits. Finally, Paul does a certain controlled unitary operation depending on the state of the two qubits here, and ping his system, system number 5, suddenly comes to the end on the identity of the state, chi, it's equal to chi now. And the Deutsch-Hydian picture essentially is a result of a no-signalling theorem. You can't have dependence on a parameter chosen in one region being displayed in the descriptors of systems in another region without having a continuous chain of interactions between the two. That's just a generalization, right? So what happens in this picture is that Mercury creates this integral state shared between Alice and Bob. This system comes in in the descriptor here, but this system 1 depends on the parameter theta. Given this interaction, the state of this system, the descriptor of this system now depends on the parameter theta. But this one doesn't, even though the two are entangled. And that follows with no signaling thing. However, when we have these two systems out here, these two have interacted, so now both depend on this parameter theta. When we have an interaction between these two and the two message qubits, that's now coming from a parameter theta. And we just take these down and do this interaction, and then it's no surprise that that couldn't come to the parameter theta 2, which had this continuous chain of local interaction to carry that information, if you like. So that's the picture for Boyd-Chapinian. They say, look, we can see exactly how the information about the unknown state which is Bob, not through non-local influences allowing it to fly across the entanglement, not by travelling backwards in time and then forwards again,

20:00 not through action at a distance, in the message of Jupits as they travel from A to B, as of O. So here we seem to have two competing accounts of the nature of quantum information. Each characterises quantum information in a different way. They say, look, it can either be this thing which can sometimes flow in a pantomime fashion backwards in time. George Payne is saying, no, no, it flows more simply. It's saying flows more simply because it can be hidden and inaccessible to local measurements. So how can we decide which one of these two competing views of the nature of quantum information is right? How does this stuff really end up? But it's at this point that we need to calm down and take a step backwards and think about precisely what we're doing. Because I think the suggestion that there's a debate between these two parties, The question that can be posed, that can be answered in either one way or the other, is to make just that mistake that Scorson warns us of at the beginning. Why so? The question that's causing us the problem is how does the information get from an answer to the problem? We need to look at this question more closely. What can it actually mean? Now, it has a very clear meaning in one sense. This is a perfectly legitimate, very clear, particularly unproblematic meaning. Could mean, look, what are the causal processes or what are the physical processes that are involved in the transmission procedure? Just what are the physical changes in the systems that go on as this protocol unfolds? That's a simple, straightforward question. Not the legitimate question of how does the information flow from us to Bob. That's not the question that George and Hayden and you from Penrose are answering. They're asking a different question. They're saying, how does information behave? But I think that sort of question is simply a mistaken one. It's a mistake to take the question of how does the information flow of the mouse devolved as a question regarding how information is construed as a particular or as a substance of channels. And the very simple reason that the term information is an abstract noun and so it doesn't stand for a entity or a substance. And this immediately dissolves the problem that we had. So when we consider an information transmission protocol, and this could be just an ordinary one, it could be one using entanglement, we shouldn't feel that we have to provide a story about how some thing

22:30 that the information stands for travels from A to B. Because the role of term-like information isn't to stand for something that exists in the world, in the physical world. And if it doesn't stand for something that exists in the world, then no more do you need to ask whether the supposed thing took a spatio-temporary continuous path or not. It isn't the sort of thing that can have a spatio-temporary location at all, so it's simply a misposed question to ask, does it play spatio-temporary continuously or not, and it's mistaken to insist that it ought to. So we need to be aware of the logically grammatical status of the term information in order to distinguish focus questions The bogus question is, how does quantum information flow? The good question, simple, straightforward, what physical processes are involved in the protocol? So when we recognize that information is an abstract now, we see that when we're analyzing some information protocol like teleportation, we don't have to do two things. We don't have to A, describe the physical processes by which the protocol is achieved, and, B, trace out the path of this strange, particular information. Because then we have a task A. That's what we need to do. Now, at this point, some of you may be worrying. Let me some justification. Right, so I'm interested in information as an abstract now. So it doesn't sound like something that's in the world. Or something that's a spatial general location, or something that can be said to flow on the side. So if I insist on that, then it doesn't matter how to move the subject matter You know, what's this theory about if information isn't something in the world? Well, before moving on to that, to answer that question, there are in fact two answers I'm going to give you. We need to look at the arguments for abstractness in the first place. So, I take it that it's clear enough that information in the everyday sense, and which is a semantic and epistemic term, is an abstract noun. Just as knowledge is abstract, information is abstract, I take it as unproblematic. But one might have a worry, right, because we should insist on a very sharp distinction between the technical notion of information that we have in the Shaman theory and the related notion in the quantum information theory from the everyday notion. These are utterly distinct concepts. And I think they really don't have very much to do with one another at all.

25:00 So I need to argue that information in a technical sense is an abstract noun too. And I think there are two very good arguments you can give for this. But first let's think a little bit, I need to say a little bit about what abstract nouns are. So the most characteristic feature of an abstract noun is that they don't stand for things having a spatiotemporal location. that's the really the central and most reliable discovering whether something's an abstract noun or not so consider truth and beauty truth doesn't have a location in the world and beauty doesn't have a location in the world although people can be beautiful, people are concrete things that have an abstract beach in their beauty sometimes abstract nouns are said to denote things that lack causal power they aren't causally efficacious or that are non-receptible these two are pretty ropey as a way of So, for example, beauty is an abstract noun, but I'm pretty sure that beauty is perceptible. Here's another useful one, that abstract nouns are often derived as grammatical nominalizations of particular adjectives or verbs. So that's what happens in the case of truth. The fundamental notion is the adjective true, we get to go from truth to truth. with information in the everyday sense but what's fundamental is the verb to inform we go from to inform to information and we explain what information is in the everyday sense by reference to the verb which is a modernization that's another story I need to answer this question what is information in your technical sense? and there are in fact two sorts of answers two closely related but rather distinct types of answers questions what is information in your technical sense? The first is, what is quantified by the Shannon information or the long line of entropy? When we answer that, we'll see that yes, information is abstract, information is still an abstract The other type of answer related to Sphinx is that information, in the technical sense, is what is transmitted over a communication channel, quantum or other ways. More precisely, is what is produced by an information source that is required to be reproduced Notice that this is a very coarse-grained definition. I haven't said what success means.

27:30 And that's deliberate because we can have a slightly different relation of information depending on what we think success in a protocol amounts to. And success in the quantum and classical cases will be very different. So this open textual definition is enough immediately to give us a definition of quantum information and classical to achieve in the protocols. So I hope you'll have time to see that. So Shannon, of course, in 1948, really set the seal on this issue. He provided us with both the notion of an information source and the notion of compression. So let me just draw up these familiar sorts of pictures. So Shannon, the notion of information source It's just some black box which has certain outputs. And let's say we have outputs of certain letters from some simplicity finite alphabet, letters A. Good, so we have this alphabet of letters that can be produced by the source. And they're produced with some probability. I'm not actually going to come out of here, some sequence of letters. Now, Shannon pointed out that if you have this probability distribution, in general there's a certain sense of redundancy in this sequence, it can be compressed down, and that's what the Shannon information age, if I call this source A, source characterised by the argument Again, the probability distribution here. The shadowing quantity... ...probabilities of the inverse times the number. That quantity measures how much the output can be compressed. So that's one sense of information. It's a property of the source, and it tells you how much the output of the source can be compressed. Now, how much something can be compressed? Remember, one of our questions is what is information? quantified by the Shannon information quantity, or is quantified by the Shannon information quantity in the context of the communication channel, is how much the output of the source can be compressed. Now clearly, how much something can be compressed is an abstract thing, much

30:00 like the size of my shoe is an abstract thing. So the shoe is a concrete object, which has various properties, but its size is an abstract thing. It's not something that lives on the end of my foot. When the shoe's on the end of my foot, its size isn't. Similarly here, of the source. The source is a concrete thing that lives in the world. It's compressibility. Compressibility is an output. It's an abstract thing. It doesn't mean that you give us one answer, yes, to information. In terms of the sense of the challenge here, it's an abstract thing. So, having got the notion of information source... Excuse me, excuse me, but the size is a property. It's an ultimate study. For example, I can use a shoe or collect some wood. And depending on the size, I can collect more or less work. So, it can't be less accurate or not. You said the size of a property. A property is an abstract. It's not a leaf, but a problem. A property is an abstract. A property doesn't have a spatio-temporal location. Okay, but you used the word abstract in abstract sense. Well, I said a property doesn't have a spatio-temporal location. It's becoming accurate. Oh, that means. Okay. Okay, numbers don't have a stociotemporal location, properties don't have a stociotemporal location, properties are abstract, particulars are concrete. And the size of a shoe is a particular part. No, the size of a shoe belongs to a particular abstract. There's one usually set, wasn't it? Well then, you don't confuse the object of predication with a predication. The object of predication cannot be the complexion. Predication is the way under which I understand the problem. The problem is effect. The predication is to make a certain move. It's to say that a certain property applies to something. Excuse me. The issue is the way that, under which I understand, I can catch a property, but the property is in fact. No, that's not very bad in the discussion. It's clearly false, not a property is in fact. I mean, that's just a category. Properties don't have special implications in predication. That's enough for me to say they're out there. Anyway, so quantum information source. It's a simple generalization. It's simple when you see it. It was quite clever to think of it, which Schumann and Heron was just thought it was. We just generalize this straight away. Simply by many of you have time to treat the simplest case today. We have a source that outputs instead of systems instantiating some letter, we have certain systems in various quantum states.

32:30 Again, this is what we're going to have at the output here is some particular sequence of systems in certain quantum states, and so on. And we can again talk about compressibility of this sequence. What resources do we need to send it on and recover it later on? Now, it turns out compressibility is going to be given by the model line entropy, which of course is very closely related to the Shannon entropy, where the density operator rho is simply given by Neumein-Entropy's probability distribution of these pure states is just the convex sum of the pure state projectors. So that's the quantum source with its output. And the Neumein-Entropy measures how much the output of this source can be compressed. And again, compressibility is an abstract thing, not something that's actually living in the world, although one that's true of lives in the world. Okay, so that's kind of an easy argument for why information in a 10% is abstract now. There's a more interesting argument with a sort of side differentiation of information. In order to understand that, we need to say, well, what do information sources produce? And to get clear on that, we need to be first of all clear on this little piece of philosophical jar and the distinction between types and tokens. This may be familiar to about half of you, and maybe not to the rest of you. So the distinction between types and tokens was introduced at the turn of the 20th century by C.S. Perks. I'm just going to illustrate it with a quick example. So if I write down the word the on the talk, and write it down once, I can write it down twice. In one sentence I've written two things down, and in one sentence I've written one thing down. The one thing I've written down is just the word that I just... What I've written down to all is two different instances of the word the. So, the tokens are the two different instances of a particular type, mainly the word the. Now, tokens are things which live in the world. Types are abstract things, so the word the doesn't live in the world, although all its utterances and inscriptions do. So the token of a particular type, there's going to be some concrete physical object here that's going to have a pattern of chalk marks on the board, but in Stansky it's an abstract thing, namely a particular type.

35:00 So if you have this use in language, it needn't be tied to, the type-token distinction needn't be tied to linguistic phenomena at all. or we can use it for our friendly sequences states here. So what we have is the output of, say, particle information source on a given run, long runs for the experiment. There will be some particular sequence of letters. Now, that would be a token of a particular type. We can name the type, so you could say, OK, this one happens to be sequence 723. The name of sequence 723 is the name of the abstract type that these particular systems having this table with the letter A, A1, A2, A3 written on. These tokens instantiate this particular type, sequence 723. Now when we say that information is what is produced is required to be reproduced, what is reproduced is the type. what is transmitted. We don't point to the concrete, well, we may point to the concrete physical object, but we're not interested in the concrete physical objects in the stand-seeing. We're interested in what the type was. We're interested in whether it's sequence 723 or sequence 7924. We're talking about two different abstract things. So we don't answer the question, what was transmitted, by referring to or describing, demonstrating, or pointing to a token of a type. We can describe the type or name the type, or we can show the type by pointing to a particular instance of it and then someone can read off and see what the type was. So this is why information, in the sense of what is produced by an information source in the classical case, is still an abstract noun. But what is produced, what we need to reproduce, is the type. We do that by doing such stuff with tokens, but in a sense the tokens aren't the interesting thing. And then we play exactly the same role in quantum information. When we have a pure state case, in terms of the case, it's more interesting, but just now just a pure state case. What we have coming out is a particular sequence of systems in some quantum state, in various quantum states. So the type that's been produced is some particular abstract sequence of public space states.

37:30 So that's the quantum information that's been produced by the source. very similar to the cancer cases of erect generalization. What we want to be an result of the transmission procedure is to have another sequence of the same, another token of the same type, another example of systems in that sequence of states. But what was transmitted, the information transmitted, is given by specifying the abstract sequence. So that gives us one answer to the question, do we still have a subject matter for quantum information theory? We certainly do. We have a subject matter in the abstract. We can be interested in the structural properties of various types. And the structural properties, of course, are sequence of Hilbert states quite interesting. So that we are interested on the theoretical side, perhaps, of the logical side of quantum information theory. We'll be looking at structural properties of these various types. And when we say things like, for example, that quantum information can't be copied, it can't be cloned, and so on, what we're talking about is about structural features of specific sequences of states. Okay. So that's the argument that was produced by sources abstract, that information in the technical centre is going to be more produced by information supports. So, I think that will establish that information, even in the technical centres, is still announced right now. With that in place, we now have to move back to addressing the legitimate questions that still remain about teleportation. so we don't have the focused controversy about how some pseudo-substance information flips around we look because we're no longer confused about the logical status of the term information but that's not quite enough to still all the controversy that remains about teleportation but that controversy that remains is of a very familiar kind, it's totally straightforward it's a recall a legitimate question that we can ask is what are the physical processes involved in the transformation? There are two distinct questions. What are the physical processes and how is information about it? It's only the genuine question. What are the physical processes involved? Now, of course, this question about which there is dispute simply depends on what interpretation of quantum mechanics want to do. And that's where the dispute lies. If you have a different interpretation of quantum mechanics, you will have a different description of the physical processes involved in the protocol.

40:00 And so, that's such a familiar level of controversy, it can hardly be said to be a controversy or confusion about teleportation. There's nothing problematic about teleportation per se. We can disagree about what's your favourite interpretation of quantum mechanics, but once you fix that, the physical processes involved in teleportation are taken straight forward. In particular, these are the sort of questions that one can get today, some would say, oh, the one-way county is involved in teleportation. Some say, no, no, it isn't. You'll get a different answer to the question of whether a one-way county is involved in teleportation depending on what interpretation of quantum mechanics you're involved. The other sort of particular question you'll get a different answer to is the one on whether anything interesting happens at Bob's side before Alice sends her a cubit. Him, a cubit, sorry. You'll get a different answer depending on what interpretation of quantum mechanics you're involved. So, very briefly, in the collapse theories here, the orthodox theoretical Neumann of the more honest GRW dynamical collapse theories, the physical mechanisms are straightforward. We know that in the collapse quantum mechanics, you have genuine non-miracle action at a distance. So the physical driving force of the teleportation protocol is simply that, it's action at a distance. you might think actions of distance is curious perhaps it is, perhaps it is and I'm not too flustered for whether established physical theory postulates it you know, just put up and shut up anyway, but they might collapse for other reasons but the point is, the mystery doesn't rest on how information is covering all we say is there's a physical process that collapsed that prepares Bob's system admittedly non-locally, admittedly instantaneously but it generally prepares Bob's system someone of four states. That's pretty much all there is to say about the physical processes involved. Clearly non-locality is involved, and clearly something interesting has happened before, as it's sending out a measurement of 12. So airbrush, of course, is completely different from collapse theories, because it doesn't have any collapse. So you're not going to have non-locality in the sense of being brought about by a collapse mechanism. So what drives the teleportation protocol and the error's interpretation is a very interesting fact that when you have a big entangled state, local operations on one subcomponent can have

42:30 a highly non-trivial effect on the global state. So a very simple case of superdance coding. You have one of the four bell states do a power lead twiddle on one side to flip the The global station is one of the other three orthogonal states. So a local operation has the biggest effect you could possibly have on the global state. Teleportation can be seen in a related light. So that's really the effective mechanism in Everett. And arguably there's no non-accounting involved in Everett at all in its account of teleportation. But there's sort of a cross between the two, so we have no collapse. Of course we have our multi-hidden variables that behave unlegantly. and highly have a nice analysis in the bone theory. And what they say happens in teleportation is that there's a non-local quantum torque that operates on the spin of Bob's system. And when Alice does her measurements, makes the spin of Bob's system flip up to some definite state. There's something interesting that's happened before. Alice sends her information to Bob. Bob's spin has acquired one of four definite spin states. And then, finally, this isn't a complete listing that gives you a flavor of the sort of options you have. This is, I guess, the dullest interpretation of quantum mechanics, in which you have the formal instrumentalism where you say that all the quantum mechanics tells us is about probabilities of measurement results on an ensemble. So there's nothing more. There's nothing about individual systems. Now, this interpretation is relatively unproblematic and particularly doesn't have any non-mechanics involved in it. it refuses to say anything. So all that happens under this sort of interpretation in teleportation is that Alice does hurt a bit, Bob does his a bit. And at the end all you say is that well, the main results I expected analysis system were such and such, and now I think the same for what system. But highly non-exciting with also non-locality. So you pay your money, you take a choice. But the point is, the story about teleportation for each one of these individually is totally clear. There's no more controversy apart from which one of these do you like. Right, so conclusions quickly. I've argued that the puzzles that surround teleportation arise from hypothesizing an abstract noun, namely information. I've argued that information in the technical sense is indeed an abstract noun.

45:00 but also they're still perfectly bona fide a subject matter of quantum information theory. In particular, we can look mathematically at the study of the structural property of types, such as sequences of quantum states, or we can study the physical processes that are actually involved in the transmission. So both of those are substantial bodies of interesting stuff to do. So, what does teleportation tell us about the nature of quantum information? What I would take away is that teleportation provides us with a concrete example of why we should pay close attention to the logical mathematical status of this information as an abstract noun. Because if we don't, we're going to get confused and drag off into worrying about bogus questions about how distinct information behaves. I think we should draw a general moral about the nature of quantum information in terms of the following we shouldn't conceive of quantum information theory as a theory about the behaviour of a strange new quantity called quantum information rather it's a theory about what communication tasks and also what computation tasks can be achieved using quantum systems you might say it's rather like a question of practising, it's kind of a scope issue it's not that we have of this thing, the quantum information, that's the wrong way of thinking about it. What we have is a quantum information theory, a theory about communication and computation. Here are some papers where I discuss these things in more detail. This one in particular is about Deutsch and Hayden and Proses and Comments. Okay, I'll stop there. Thanks very much. So, incidentally, a prophecy can be defined as the value of an observer or an environment. So, in my opinion, this is the most important thing that we have to accept an essence. But my question is a matter of, so far I understood the necessary requirement for something to be the correct thing is to be localized in space and time. It needs to be intelligible. Can you note that I didn't say it was a necessary condition, I said it's characteristic.

47:30 Because you're right, I guess where you're going is that quantum systems don't always have a well defined location. This is my point. I mean, this is exactly my point. I mean, it's a quantum system that is delocalized. What is the state? It's an abstract known or what? Sorry? I mean, the state is the same or the delocalized system. The state is certainly abstract. The system is concrete. even if the properties that the system in particular has mean that it doesn't have a particular location of space and time that doesn't mean that it's not intelligible to apply in general to that type of system predicates of spatio-temporal location so what we need, we're denoting logical categories so what we're looking about is general types of things can be intelligibly stated. So, in general, it's intelligible to say all systems, whether or not they occupy certain spatial-semple locations. Excuse me. Sorry. I cannot conceive of a system that cannot be in a given state. How can you conceive a system that is not in a state? How can a system be in a state? Well, that sounds like a confusion between mathematical and physical. The state is a mathematical object, which denotes the properties that the system has. The properties are also abstract, but not mathematical, really. The concrete object is the thing which the various properties can be truly or false in sets of hazards. I think, Peter. Well, I feel that if one carries on that sort of, to the end, this program of non-hypothesizing astronauts, that physics will become as dull as statistical interpretation is. Because something which this is, I think, valid greatly is heuristics, which comes from short hands, with short hands, that's how they make moments, so I do see what you're saying philosophical, but I also do see that there is a great realistic value in calling teleportation, teleportation, because according to you, one should really sort of ban a disturbance,

50:00 not being teleportation. No, don't worry, I'm quite happy saying teleportation, but I would quite say, well, yeah, so here's so one needs to assess them on two axes. One is how pecunded they are, how much they give rise to you. The other is whether or not they give rise to confusion. My claim is that conceiving information is a kind of stuff that gives rise to irreconcilable confusion. Joseph Henry said, does this? No, it does this. That debate can't be decided because there isn't a genuine question to be decided. Sometimes, okay, so an interesting contrasting case is a term like caloric, right? So caloric is a putative substance referring term. Turned out that it wasn't, after all, a referring term. There's no such entity as caloric. Now, my point is that information is never, was never, and never should be, seemed to be an address to caloric. So caloric was introduced as a putative substance referring term. Turned out it doesn't exist. Okay, fair enough. information simply doesn't have a role of a substance referring term. So it's not about saying it's just saying it. So there's nothing wrong with saying here's some term, theoretical term, I take that to be a substance referring term. The point is that information in the way in which it has a genuine beneficiary use, in the way it's introduced there, it simply doesn't have that role. But you're right, I mean, one needs to be a little bit careful with these positions. I'm just thinking that, again, this is the thing about information all their work time, heuristically take information to be, well, not referring to a substance which is kind of a primitive, you know, primitive notion in all the answers. You can just talk about this. Yeah, I'm just trying to sort of establish physicists' everyday work in Illinois. Thanks. Well, I agree with you, Chris, and I just want to tell you a joke. When I was sitting here, I realized that there is a sort of analogy you can make with, you took the result of the knowledge, you know, I was trying out, of love, and you can actually make a pedagogic analogy with Abelard, sending Eloise a letter, which says, I love you. and you can raise the stupid question, how does the love get to Eveline's? That sounds like a wrong question.

52:30 Because love is an abstract man. If it's a good question, let's investigate the process, the physical process. That can be analysed in various ways. There's the theory of post-print. There is also, however, the ordinary answer. They both understand medieval French. And there is then a deep question, which we get in philosophy of mind and language, about how sounds or ink on paper sustains meaning and how mental life and legal language interact, and there are states that are required, Wittgenstein, And so it seems to me that there's an analogy here, because insofar as you think that Deutsch and Hayden, when they're not explicitly theoretically enough, it's a conventional quantum mechanical that lies in both picture description. That's like the commonsensical answer. The luck gets there, if you want to talk about it, because they both understand medieval French. And the controversies of Collapse versus Poe versus Everett, it's like the endless controversy in philosophy of mind and language about 100 pages of what's going on. And I would even say that the dear, great Roger Penrose is, well, the love got there because of this background interaction, you know, that's, it was, you can only explain how she gets people's love by reading this inscription by referring to their previous interaction. Actually, that's a causal ring to it, because, arguably, you couldn't send someone your love unless you were already in a loving relationship. But you couldn't announce it. Yeah, good luck. That's really helpful. I think it's an A for a black instead of A for an artist. Symmatricist. That's good. You might find it. I think this analogy is misleading, in a way, because it's not, I mean, Alice knows nothing about the state. I mean, neither does Paul want to excuse me to state. I mean, not at all, like, reading something off, like, I love you or so, it's...

55:00 No, no, I mean, that's true, so that's... I mean, that's the difference between the structural properties of the classical sequencer and the quantum sequencer. So here's an interesting point. It's not because people want information, but what Victor knows about the state. No, no, see, that would be information in the everyday sense. That's not the notion of information it's in play. If you've got an agent who knows something about the state, that's the everyday notion of information. That's the translation. It's not quantum magic. Well, the analogy is just an analogy, right? It's very . I think the thing is, in a certain sense, there's a common pattern between a silly story and the part of the racist story. But it is, of course, very puzzling, as you bring out. And that's why you need to go through the detail of Deutsch Haven or some similar description. Yeah, I agree. There is a puzzle there that is not there to bring that to life. You know about the rock spectrums, the rotation of the world, which if you look at the initial list of puzzles, it shares all of them. It's utterly not a puzzle, because what's transmitted is the probability, that somebody has about, first of all, say a coin here and a coin there. That's analogous to the instrumentalist answer to what's going on in sort of EPR or interpretation. So in a sense, sure, it's unproblematic. But that's what the analogy is. So if there's another semi-probability distribution. I have a list of analogs that actually is shared as classical, obviously un-classical example. Well, not quite all of them, so there's no classical analog of the amount of information that's transmitted into them. Yes, absolutely, because if your redistribution would be anything. So, if it's p and 1 minus p, or, say, that's running x, then this number is just a real number which is transmitted in the same sense. Yeah, I mean, strictly speaking, we need to be careful when we talk about things like transmitting states and transmitting probability distributions, because those things are abstract too, so we can't actually think of them tracking through states. Doesn't that depend on your interpretation of whether the states have to go?

57:30 I suppose we can transport these questions into the lunchtime. Thank you very much.