Everyone is speaking of it, part II

The more I hear about this result, the more I fear that the media have picked it up only because they misread the meaning of the title… Let me explain what is done there as simply as I can. I’ll let the reader decide if they think the media could have understood this šŸ™‚

Let L (lambda in the paper) be a list of deterministic instructions of the type {“Measurement A –> give result a”, for all measurements}. Since quantum states do not predict deterministic results for all measurements, a single list is trivially inadequate. But there is a very natural way to generate randomness: just pick different lists {Lk} with probability pk each. So, the model is:

Quantum state of a single object <–> {Lk, pk}.

What the paper proves is that no two quantum states can share any list: the set of lists with probability non-zero uniquely identifies a state. In other words, giving the possible lists, or even just one of them, is equivalent to describing the state…

… for a single object! Indeed, Bell’s theorem proves that not only a product of lists {La,pa}x{Lb,pb}, but even a single product list {LaxLb, pab} cannot describe entanglement. So, lists just don’t seem to do the job. Personally, I can’t believe that the randomness of one quantum object comes from a list, when we know that the randomness of two quantum objects cannot come from a list.

In the same vein, I have a small problem with the logic of the proof. One constructs a family of product states, which should be obviously described by products of lists, and measures them by projecting on a suitable family of entangled states, which… which… wait a second: how does one describe entangled states in that model?? It seems that the closest attempt was Spekkens’ toy model, which reproduces many nice features of quantum physics, but unfortunately not (guess what?) the violation of Bell’s inequalities. Maybe the contradiction exploited in the proof comes from the fact that there is no description of entangled states in a model with lists?

That being said, this paper does add something for those who still were trying to believe in lists as explaining quantum randomness — and the more this idea is shown to be inadequate, the better šŸ™‚

Note added: I was convinced that this post misses the point, but it triggered some nice follow-up; so please read the subsequent thread of comments: the “truth” may be at the bottom — or in the exchange šŸ˜‰

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About valerio

Principal investigator at Centre for Quantum Technologies and professor at National University of Singapore

Posted on November 28, 2011, in Common knowledge, Latest topics, Philosophy. Bookmark the permalink. 4 Comments.

  1. I also don’t find the result very surprising, but then again I am sure some people said that about Bell’s theorem in the sixties (and with some justification, e.g. Bohr was already sure in 1935 that the EPR program wasn’t going to work). I think it’s good news for Bohmians because it means that there is a good reason for the form of Bohm’s theory (where the quantum state is part of the hidden variables). I suppose in principle it’s good news for people who like many worlds (like me) as well, but I think they will probably care less because they were already convinced.

    I am not sure I understand your comment about product vs entangled states. If the hidden variables are doing their job, then they have to tell you the outcomes (or probabilities of outcomes) for all kinds of measurements, including those that quantum physics describes by entangled states. It makes sense that the impossibility proof makes use of those cases, but I think that’s fair, no?

  2. Valerio,

    The lists don’t have to be deterministic. I know that it doesn’t matter for the proof Bell’s theorem, but it does matter conceptually since we want to include the case where the quantum state itself is the only beable, i.e. the orthodox interpretation.

    Also, I don’t really understand your comments about entanglement and Bell’s theorem. PBR make no assumptions about the ontic state space of a composite system other than the fact that it should contain all products of “lists” corresponding to the individual systems. It may also contain additional parameters that only come into play when we prepare entangled states, which would allow nonlocal effects to be simulated. PBR do not need to consider these parameters because they only need to consider experiments in which product states are prepared. See http://arxiv.org/abs/1111.6304 for more on this. It is a little confused, but gets the essential idea right.

    Generally, I think that a lot of people are upset by the title of this paper, which is fair enough, but I think that this often leads them to be too dismissive of its actual content. It may well be the case that nobody was taking the kind of theory ruled out by this paper seriously beforehand, but does that mean that it should not be ruled out rigorously? Did many people believe in local hidden variables before Bell’s theorem? Was it worth ruling them out rigorously?

    Too often, people are willing to make strong assertions about quantum foundations based on intuition or philosophical prejudice (insert appropriate allusion to the attitude of Bohr mentioned in the previous comment here). If we have learned anything from Bell, it should be that we should instead base our opinions about quantum theory on rigorous results and experiments wherever possible, since that is the scientific method.

    Imagine, if you will, that instead of proving their no-go theorem, PBR had actually managed to construct an epistemic hidden variable theory of the type that their result rules out. Would that have been interesting? Would it have possibly led to new ways of classically simulating quantum experiments? Would it have been competitive with Bohmian mechanics, which at least some people find compelling? If you answer yes to any of those questions then I don’t understand why it should be deemed uninteresting just because the result actually goes the other way. It places a strong constraint on how to go about answering these questions.

  3. Christoph and Matt,

    Thanks for your inputs šŸ™‚ Finally I managed to provoke some discussion!
    First, let me admit my sin: I have never made the effort to appreciate all the discussions on ontic vs epistemic, Spekkens’ model etc. It is certainly a sin of laziness, but not of blind prejudice: for me, (1) the experimental demonstration of quantum effects with individual objects and (2) Bell’s theorem rule out pretty much any statistical interpretation. Indeed, (1) rules out the ensemble view; (2) rules out the “local instructions” view.

    As a first step towards my healing, let’s see if you agree with the following:
    (i) The PRB experiment involves the preparation of product states and a “localized” measurement (which, in the quantum description, projects on an entangled basis; but this is irrelevant in the phenomenological description as you pointed it out).
    (ii) As such, it can be simulated with a classical device: I put one of my students in a room and give him a description of the measurement (a single one, so I don’t even need a student with free will). Then I provide him with N pieces of paper, each with a quantum state written on it (one out of four in the simplest example, so I need free will, whatever that means). As an output, the student produces results that are compatible with the quantum expectations.
    (iii) What PBR prove is that, in order to succeed in such a test, the student must use a formalism in which psi and phi are recognized as completely different objects. By “recognized”, I mean the following: my brain can deterministically distinguish the expression “|0>” from the expression “a|0>+b|1>”, even if nobody can deterministically distinguish in which of those states a quantum system may be.

    So, in one line, PRB prove that “|0>” is really and entirely different from “a|0>+b|1>”. Correct?

    If indeed this is correct, then I have learned something interesting indeed, which could not follow from (1) and (2) above.

    At this point, my only concern would be about the meaning of an experiment… I mean, I can publish an experiment tomorrow myself, I just put one my students in a room and… šŸ˜‰

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