## The quantum state cannot be interpreted statistically?

another, leaninng to the epistemic view (can be treated statiscally)

Epistemic view of states and communication complexity of quantum channels
http://arxiv.org/pdf/1206.2961v1.pdf

...The main motivation of this paper is to show that ψ-epistemic theories, which are attracting increasing interest in quantum foundation, have a relevant role also in quantum communication.....
 becoming a trend Physical Review Letters. 109, 150404 2012 Distinct Quantum States Can Be Compatible with a Single State of Reality http://prl.aps.org/pdf/PRL/v109/i15/e150404 ...rather whether there are multiple wave functions associated with a single real state. A natural way to understand this is as an expression of the second kind of epistemic view above—that a quantum state represents an agent’s information about an underlying reality but is not part of that reality itself... MathOverflow Psi-epistemic theories in 3 or more dimensions http://mathoverflow.net/questions/95...ore-dimensions ...yes, maximally-nontrivial ψ-epistemic theories do exist for every finite dimension d... Physics Stack Exchange The quantum state can be interpreted statistically, again http://physics.stackexchange.com/que...in/36390#36390 ...by the way the options are: .-only one pure quantum state corrrespondent/consistent with various ontic states. .-only one ontic state corrrespondent/consistent with various pure quantum states. .-only one pure quantum state corrrespondent/consistent with only one ontic state.

 Quote by Fredrik Their argument against the second view goes roughly like this: Suppose that there's a theory that's at least as good as QM, in which a mathematical object λ represents all the properties of the system. Suppose that a system has been subjected to one of two different preparation procedures, that are inequivalent in the sense that they are associated with two different state vectors. Suppose that these state vectors are neither equal nor orthogonal. The preparation procedure will have left the system with some set of properties λ. If view 1 is correct, then the state vector is determined by λ, i.e. if you could know λ, you would also know the state vector. Suppose that view 2 is correct. Then either of the two inequivalent preparation procedures could have given the system the properties represented by λ. Yada-yada-yada. Contradiction! I haven't tried to understand the yada-yada-yada part yet, because the statement I colored brown seems very wrong to me. This is what I'd like to discuss. Is it correct? Did I misunderstand what they meant? (It's possible. I didn't find their explanation very clear).
An example of inequivalent preparation procedures which lead to undistinguishable states is easy to construct in standard QM. You can prepare, using simple dices, states with probability p1 in ψ 1 and p2 in 2. This state is described by a density matrix. But the decomposition of a density matrix is not unique, so you can prepare the same density matrix in a different way, preparing other basic states 3, 4 with other proabilities.

Suppose now you find a theory where the hidden variable λ uniquely defines the density operator ρ. Then, the two different preparation procedures give the system the same observable properties as the state of the hidden variable λ.

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I know this a bit late but this interview article discussing the important PBR theorem, was a very interesting one to read for 2 important reasons:

1. Why the paper wasn't published in the original submission even after provisionally being accepted
2. Describing the connection between their 2 papers that seem to arrive at different conclusions depending on one assumption:
 That preprint was submitted to Nature, but never made it in (although it did ultimately get published in Nature Physics). The story of why such an important result was shunted away from the journal to which it was first submitted (just like Peter Higgs’s paper where he first mentioned the Higgs boson!) is interesting in its own right.
 Now the fun started. As this revision was ongoing, two of us submitted a preprint to the arxiv with another of our students, a paper with a somewhat tongue-in-cheek contrary title: The quantum state can be interpreted statistically. Later I will explain a bit more carefully the relation between the physics of the two papers...The theorem we prove – that quantum states cannot be understood as merely lack of knowledge of an underlying deeper reality described by some as yet undiscovered deeper theory – assumes preparation independence...That second paper is, however, simply making a mathematical/logical point-it is not a serious proposal for how the physical world operates. We are in a similar position with Bell’s theorem, which I consider the most important insight into the nature of physical reality of the last century, an honour for which there are some serious competitors! That theorem relies on a presumed ability to make independent choices of measurements at separated locations. Denial of such is the “super-determinism” loophole, and while intelligent people can and do consider its plausibility, and while it is an important insight into Bell’s theorem that this assumption is necessary, the jury is still out (‘t Hoofts efforts notwithstanding) as to whether a super-deterministic theory agreeing with all experiments to date can even be constructed, never mind be a plausible theory of nature.
Guest Post: Terry Rudolph on Nature versus Nurture
http://blogs.discovermagazine.com/co...ersus-nurture/
 ...by the way the options are: .-only one pure quantum state corrrespondent/consistent with various ontic states. .-various pure quantum states corrrespondent/consistent with only one ontic state. .-only one pure quantum state corrrespondent/consistent with only one ontic state. the latest (this month paper): Distinct Quantum States Can Be Compatible with a Single State of Reality 12 October 2012. Peter G. Lewis, David Jennings, Jonathan Barrett, Terry Rudolph

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 Quote by audioloop the latest (this month paper): Distinct Quantum States Can Be Compatible with a Single State of Reality 12 October 2012. Peter G. Lewis, David Jennings, Jonathan Barrett, Terry Rudolph
Note that in the link above, Terry Rudolph does discuss that paper but he doesn't seem to take it very seriously. From the interview:
 Let me briefly explain the interesting science that lies at the heart of the “key assumption” the editor is alluding to in the above. I will call this assumption preparation independence. Suppose an experiment at one lab reproduces the results of an earlier experiment at another. This would righty be called an “independent” verification of the first lab’s results. No scientist would attempt to refute this by appealing to correlations between random events at the two labs, there being no realistic mechanism for such to be established. Even in a single lab, repeated runs of an experiment must be assumed independent in order to estimate probabilities based on the results. Preparation independence is simply the assumption that we have the ability to build independent, uncorrelated experimental apparatuses to act as preparation devices of microscopic systems, and that any deeper theory of nature than quantum theory will not overthrow this principle by virtue of “hidden super-correlations” where to date scientists have always successfully assumed there are none. The theorem we prove – that quantum states cannot be understood as merely lack of knowledge of an underlying deeper reality described by some as yet undiscovered deeper theory – assumes preparation independence. It is an important insight that this assumption is necessary for the theorem, and the point of our second paper was to show this explicitly. That second paper is, however, simply making a mathematical/logical point – it is not a serious proposal for how the physical world operates.

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 That second paper is, however, simply making a mathematical/logical point – it is not a serious proposal for how the physical world operates.
It's good to know that.
 Blog Entries: 19 Recognitions: Science Advisor A recent explanation of the PBR theorem at a level suitable for a general physicist audience is presented here: http://www.physicsforums.com/blog.php?b=4330

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 ..."Does there exist a maximally-nontrivial ψ-epistemic theory in dimensions d≥3?"... ..."The answer to my (and Lewis et al.'s) question is that yes, maximally-nontrivial ψ-epistemic theories do exist for every finite dimension $d$"... http://mathoverflow.net/questions/95...ore-dimensions