Quantum information does exist

0:00 And then reproducing those properties over at Bob. And if he knows the appropriate decoding procedure, then maybe he can discover the message that was intended to be sent. So you can think of dense coding as the obvious example here. But in order to transmit classical information, We have to appeal to this quantum concept of information because without this property preservation or correlation or about sense, we're never going to get classical information transfer either. So maybe that gives one reason for thinking that this is a non-trivial matter of definition or something like that. What's information in this story? And there surely isn't much. Wouldn't that be fair to say that this is just a very clever way of getting classical information across a channel? And how to do that? Is that exactly what this theory figures out? This is obviously highly non-trivial. I mean, I'm not suggesting that I think that this is banal. I mean, that's what I'm saying. I'm just trying to explain what the information is. Yeah, I mean, I think that that's fair, but I mean, in another sense, look, we don't we don't even have to mention classical information here at all. I mean, take teleportation, for instance, right? There's no classical information transfer in quantum teleportation. You take an arbitrary quantum state, you move it around. I mean, you can talk about the ways that might be used to transmit classical information, but that's not fundamentally the goal. With that sort of process. First of all, it would be interesting for you to say a few words about the, you skipped over, the sort of leakage at the bottom of conventional information theory over issues like the existence of a message. I think you mentioned a problem, you know, very big. If you have a very large transmission resource with very little information going through, you get to mathematical limits of determining whether you have a message or not.

2:30 Oh, that sort of stuff, if you could leave that one for a moment, that's just a small issue, I would like to hear comments on that. The bigger issue is, perhaps the other way round, in saying, do these processes which you're regarding as being expressible in terms of resource, do they submit? Including the sort of process like your process that emits spinning tops and things. Do they submit to what would be an engineering approach of saying if we describe them in some way we can name an entropy that would get you within what you might call a tolerance of the description and that if you keep on working at it you can get nearer and nearer and nearer you're never going to get all the way there. Does the process submit to that type of mathematical approachability? These are not properties of themselves, which, I guess, are not quite clear in your question, so is the question something like, there's a theoretical limit as to what resources are required to transfer these properties? Well, given a resource of such coupling error, I suggest the word coupling, I don't know, so you could run a process of some sort. Use the description of what is happening. It has to be selected as basic as possible. And you would need to describe things at some length in order to pick out and say what the relationships are. Now, is it that type of process where... Oh, okay. I think I'm getting clear on what you mean. No, no, no. So let me see if this is what you're asking about. Suppose that we have a description of the quantum system, okay? Does that change the resources required for transfer? Indeed, the resource I presume can be described in practical terms, but it might not be definable in every sense, because the binary digit is a terribly convenient thing, and when it comes to the states of typical resources like a piece of copper wire, for instance, let alone anything else, you don't describe it with a few binary digits, by any means, so the resource itself might be describable, but not in that discrete or complete way. That seems to me to leave open a big space there.

5:00 And then the problem of describing what's happening would never, it gets that engineering problem back again like the one you described. It's almost like saying a TV picture is not the reality but it gives you a part of the reality and then if you get a better TV picture you'll get a bit more of the reality sort of thing. Does that type of approach to a limit apply in these cases? No matter how well you describe a quantum system you're not going to get property transfer in the sense that I've described here for the following reason if you want to transfer entanglement from one system to another you have to have a local dynamical coupling to another system. I can't simply describe this coupling take this description even if it's complete and then Change a system over at Bob's such that this entanglement is preserved. So the description, again, even if it's complete, simply won't get the job done in terms of transfer of properties. And it should be mentioned also that in the quantum case, a blind coding procedure is the optimal one. Knowing doesn't help us for precisely this kind of reason. Did that do it? I see roughly where you are, I think. Can I just carry on for a moment? It sort of feels as though I was trying to set the question the other way around. Is the situation that can be supported by the resource... In other words, can we put an entropy limit on the transfer of information you can get through such a resource under some terms? Oh, yes, absolutely. It's very clear what the limits are. Yes, you can prove that right off. There's a well-known bound called the Holivaux bound, which limits the amount of classical information one can extract from a quantum system. It turns out that you get one qubit, or one bit per qubit, which is strange because qubit is a continuous system. We can store an arbitrary amount of information in it in the sense that we can correlate a qubit to a choice that we make.

7:30 You can conceive of it quite easily, in some sense, in a way that you would never be able to describe. But no, I'd say just the opposite. In a classical case, we could describe it. Because in principle, we can measure the states of each one of these spinning tops, precisely. And if we transfer that description over to Alice... I wouldn't say that, because I would have thought that's the one thing you can't do with a definition of measurement. You would need an infinite amount of information to describe it, so therefore you can't. There's a number of things to say there. Yes, in some senses it's true that we would need an amount of information to describe some arbitrary parameter, continuous parameter, that's certainly true. But the game you start out with, right, is you have a fixed set of states, a finite fixed set of possible states. So, yeah, it's only an approximation anyway. Right. I mean, then we could... I would suggest, in that case, what we would do is we'd have this kind of classical notion of fidelity, whereas if you get, you know, come so close to the actual state, then that's good enough for this kind of classical physics information transfer, the transfer of the spinning tops. Oh, the first point you could argue, too, about that would be the leakage at the bottom of the convention. Leakage. I don't want to use that word, but I think what you're keying into is, here's what I wanted to say, I don't know if I said it or not, that look, you take an arbitrary electronic signal and there's nothing you can do to that signal that will tell you what the information content of the signal is. There's nothing physical about the signal that says I'm carrying information.

10:00 It's only relative to the encoding that you can tell anything from a signal. In this sense, there's no reason to suppose that information attaches to a particular physical system. The way it attaches is in virtue of a relational property it shows to another system. Just like, for example, velocity. Velocity is a relational concept. I can't tell what the velocity is. The velocity doesn't attach to a single system, right? It describes a relation between at least two systems. Similar here with the notion of information. Question. You said something along the lines that after a unitary transformation, the resource for transfer may not be preserved. Something along those lines. And you would think that it would be. Why is it the case that... You can do this and the resource for transfer will possibly change. Okay, I think this will make you very happy. I actually didn't say that the resources required for transfer would change. Oh, didn't you? Indeed, they don't exactly the same. Oh, I'm completely misquoting you. No, no, no, but what's going to change? Can I write on this? Yes, yes. I mean, what's going to change is the fidelity of our research. If this is one system and this is another one you deteriorate into it, the fidelity between these two systems is going to be different. So I wouldn't say that A has the same quantum information as B, precisely because the fidelity between the two isn't the same. You submit different measurement statistics for each one of these. What I would say is that because they're unitary related, the quantum information of B can be made to coincide with the quantum information of A if we do the appropriate unitary transformation.

12:30 The resources required for transfer in this case is exactly the same because this S of rho is unitary invariant. So, thank you very much for this interesting and excellent talk. Thank you. It's the pattern at a microscopic level that makes the quantum chance theory be the right chance theory at that level, and it works all over the place. But nevertheless, it may be that once you concoct a monstrous Boolean proposition based out of those fundamental events, you can get something whose frequency is quite different from... It's objective probability. Would you put one of the other limitations? Very few trials? No, no. It's just... I was claiming... Colin, if you think this is wrong, that would really be important for me to know. But I was claiming that as long as your outcome space is finite, it simply can't be the case that every proposition that you can make out of outcomes on that... All of this has a frequency very close to its objective probability. It just can't happen. Ergo, there's going to be some Boolean monsters whose frequency is different from their probability substantially. It's going to be unlikely in the frequency sense. That doesn't happen often, but it happens sometimes. It's more of a patchwork than a system.

15:00 And if you've given up the idea of what really is just like being non-human things in the book, that's okay, but since you're deriving them from, I mean, is this like a picture of how you get your systems? Sometimes you look at some areas that you're interested in, and it's just like you somehow write everything down, what happens in that area. And this is a pretty great project, but my first point is then, if you write everything down, Even if you're just looking at one local area, you can write from there, that means in different languages. But if you write from a different language, then the system is going to come out better and stronger in one language. And so you might have different systems. Even one language, presumably, with those criteria and strengths you could have. There's no infer I can't see that you're not going to get different systems from one to one side. Yeah. So anyway, conceptually there's limited possibilities and then obviously they're not going to be consistent with each other. Does that imply some kind of... Why do we even think that we're going to get one method to get one solution? Of course it matters. I think that... If sort of just looking, as you say, at one bit of things and writing down what happens in one language, if there are two or more systems that sort of tie for best and they're quite different, then that's a world or part of a world in which there's not really well-defined chances. Now, there's still going to be a sense in which you can look at where those two systems agree. Or come very close to agreeing, and they have to in a lot of things, otherwise they're going to be getting the frequencies all wrong, and a human system can't do that.

17:30 So you can look at sort of where they agree and just use that part as the chance, and that's okay. But it's going to be a strange world, not like our world, I think. And to go back to your first question, it's right that if you use sort of gruesome predicates or just a quite different language to classify what happens and describe what the actual events are, Thank you very much for your time, and I look forward to hearing from you in the future. But if you say, write down the contents of this room, just use the categories that matter to you. I won't have too hard a job of it. I'll give the name of every person and I'll tell you how many green chairs there are and how many black chairs, how many tables, how many plants, and I'm done. And then I can look for patterns, and then I can look for patterns if there are any about the distribution of people in chairs. I can't believe you'd defend a theory with so many vague terms in it. It must be a record, you know, medium, short, run, patterns even, I think, you know, not many, mostly, very much practical. But really, it's really following up Roman's question. It seems to me, if you knew that the world was going to end, you know, ten years' time or something, and you knew that there were going to be, I don't know, say in the whole history of the universe, there were going to be two billion people. The Platy and Dema will tell you something based on, I admit to you, on the assumption that you've got indefinitely iterable process, whether or not it's actually...

20:00 We'll tell you something and if they tell you something different if you knew the world was going to end then you you would go like with the with the quote pattern but of course you don't and what you've seen so far is not the pattern it's what you've seen so far and in that circumstance it seems to be clear that you go with the Laplacian demon and and take it if there were a big divergence that the pattern so far the observed frequencies so far were unrepresentative of what was really I think you're not playing fair to my kind of chance, because even at the macro level, the macro level chance is not based on anything less than the entire history of the world. So you already need a godlike entity to whisper the macro probability in your ear. It doesn't take a lot of calculation, it just takes knowing... It takes a lot of knowing the future as well as the past, that's all. And how do we try to discover probabilities? Well, we look at the patterns we can see and we do simple induction, that's all we can do. But the point is, in a sense, the whole justification of the principle of principle is predicated on a science fiction scenario to begin with. Because if somebody's going to tell you X, the chance, the objective chance, they have to have seen the entire pattern of events in the world. So, I may not, I don't have to know whether it was two billion or an infinite future history of future smokers. I don't have to know that, but if somebody tells me that the macro level probability is one half for these kind of smokers, that's what I'm going to set my credence to, because I know that the rest of human history is going to look like that. And the principal-principal, you've got a defense, there are other defenses, they all, I don't know, they all seem to, sort of beg the question in some way or another, why don't you take the definition groups and simply say, I don't believe in objective chance, but I can simulate all the distributions that arise for objective chance simply by assuming exchangeability.

22:30 And exchangeability simply arises when I think that there's no particular causal link between successive members of the sequence and so I've got an exchangeable distribution and then what I'll get then, by his theorem, is a distribution that looks as if there's an objective chance but I don't even have to assume it. So it seems to short-cut all this very nicely. You don't need any of this discussion, right? Do you think that that can work for all sorts of different kinds of... Distributions, can De Finetti get us quantum mechanics? It does, it works actually. I was at Stefan's conference last year where lots of people were saying exactly that, that it does work in quantum mechanics. I don't have the authority to say that myself, I might repeat what I heard, but I don't... It's the words without the knowledge, if you've got it. Well, I'm liking the words as well, but I think when I read a bit of original De Finetti in just a bit and where he talks about exchangeability, it seemed to me like it was cheating because the real reason why you'd ever want to make your credences exchangeable is if you're trying to make them match something that you take to be a genuinely independent objective chance external to you. And that lacking that, why on earth should I think that exchangeability is a reasonable thing for my subjective probabilities to have? Indeed, it's a rather odd thing. Because I just think that successive outcomes of a coin toss, for example, having heads now doesn't cause having tails later on. I just think that these things are causally unrelated. In that case, I would... He accused me of using vague words, and I'm going to accuse you of using vague and undefinable words. Well, at some point. Most of my words were not. Anyway, the... I don't know, I think that... Quantum mechanics and gambling devices, at least, give us probabilities that really are telling us something objective about the world. I'm not so sure about a lot of other areas, but it seems to me that it's right to say that it's an objective feature of this world. It has nothing to do with anyone's credences that the chance of a good well-flipped coin landing heads is half.

25:00 And if I give this human story, I can exactly tell you what it is about the world that makes that true. So why should I go to De Finetti route? You're assuming that I've been pummeled and bruised by this question period. Maybe yes, maybe not.