The quantum state cannot be interpreted statistically?

In summary, the Pusey, Barret, Rudolph paper of Nov 11th discusses the differing views on the interpretation of quantum states and argues that the statistical interpretation is inconsistent with the predictions of quantum theory. The authors suggest that testing these predictions could reveal whether distinct quantum states correspond to physically distinct states of reality. This preprint has attracted interest and discussion in the scientific community.
  • #491
Anyone know if the PBR paper has been published, or at least accepted for publication yet?
 
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  • #492
bohm2 said:
... some have argued that non-locality does not imply incompatibility with relativity since it may depend on which interpretation of relativity is true.
Or which definition of quantum nonlocality is used?

John Bell said:
I think it’s a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things. But I would say that the cheapest resolution is something like going back to relativity as it was before Einstein, when people like Lorentz and Poincare thought that there was an aether -a preferred frame of reference-but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether...that is certainly the cheapest solution. Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant...what is not sufficiently emphasized in textbooks, in my opinion, is that the pre-Einstein position of Lorentz and Poincar´e, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether - that is a perfectly coherent point of view...The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now if all Lorentz frames are equivalent, that also means that things can go backwards in time...[this] introduces great problems, paradoxes of causality, and so on. And so it is precisely to avoid these that I want to say there is a real causal sequence which is defined in the aether.”
Wrt the above, my current opinion is that John Bell's view was just wrong.
 
  • #493
Two more papers on this theorem. The first paper is difficult to understand. I don't understand what the author is trying to say.

Can quantum mechanics be considered as statistical? An analysis of the PBR theorem
http://lanl.arxiv.org/pdf/1203.2475.pdf

Alternative Experimental Protocol for a PBR-Like Result
http://lanl.arxiv.org/pdf/1202.6465.pdf
 
  • #494
Fredrik said:
Anyone know if the PBR paper has been published, or at least accepted for publication yet?
This perhaps will never happen after the two of the authors in PBR has somewhat contradicted themselves in
http://xxx.lanl.gov/abs/1201.6554

See also posts #485 - #488.
 
  • #495
Demystifier said:
This perhaps will never happen after the two of the authors in PBR has somewhat contradicted themselves in
http://xxx.lanl.gov/abs/1201.6554
This doesn't seem to be a reason to not publish it, since the abstract says that "The results of this paper do not contradict that theorem, since the models violate one of its assumptions". However, if it was up to me to decide if the PBR paper should be published or not, I would at least demand that they rewrite the paper. I think it's just a mess. There isn't even a clear statement of the theorem in the article, and the "proof" is extremely non-rigorous.
 
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  • #496
The author of the last paper on PBR http://lanl.arxiv.org/pdf/1203.2475.pdf posted in Leifer's blog and Leifer doesn't seem to agree with his take on it:
I don’t really agree with your take on the PBR theorem. According to Harrgian and Spekkens, and also PBR, λ is supposed to be the full ontic state of the system. If the wavefunction is ontic in the model under consideration, then it is considered to be specified by λ and is not considered a separate variable. This is the reason why the term “ontic state” is used instead of “hidden variable state” because the latter is often interpreted to be variables in addition to the wavefunction. Most people would consider the wavefunction to be ontic in de Broglie-Bohm theory. I know there is some discussion of whether it should instead be regarded as nomological (lawlike) in the literature, but this is not really relevant here. The fact is, even if we know the exact values of the position variables in Bohm’s theory, we will still also need the wavefunction in addition to the position variables to compute the outcome probabilities for any experiment because it is needed to find the trajectories. Anything you need to compute the final outcome probabilities, over and above the primitive ontology (beables), is considered part of the ontic state by PBR by definition. You might not like that definition, but by using it we see that one feature of Bohmian theory is actually necessary for any hidden variable theory, namely that the wavefunction is ontic (in the sense of being required to compute the probabilities of any possible experiment). Therefore, Bohmians should be pretty happy about the PBR result as it vindicates one of their assumptions.

Also, I just wanted to note that I do not understand your discussion around eq. (10). Why do you think we can always replace a qubit state with one that has equal amplitudes up to a relative phase?

Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/q...-the-pbr-theorem/comment-page-1/#comment-2618
 
  • #498
I thought I'd post these PBR-related papers here for reference:

Physics papers:
The quantum state cannot be interpreted statistically (original PBR paper)
http://lanl.arxiv.org/abs/1111.3328

Generalisations of the recent Pusey-Barrett-Rudolph theorem for statistical models of quantum phenomena
http://xxx.lanl.gov/abs/1111.6304

Completeness of quantum theory implies that wave functions are physical properties
http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.6597v1.pdf

The quantum state should be interpreted statistically
http://lanl.arxiv.org/pdf/1112.2446.pdf

Alternative Experimental Protocol for a PBR-Like Result
http://lanl.arxiv.org/pdf/1202.6465.pdf

The quantum state can be interpreted statistically
http://lanl.arxiv.org/pdf/1201.6554.pdf

Can quantum mechanics be considered as statistical? an analysis of the PBR theorem
http://lanl.arxiv.org/pdf/1203.2475.pdf

On a recent quantum no-go theorem
http://lanl.arxiv.org/pdf/1203.4779.pdf

Popular:
Quantum theorem shakes foundations
http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392

PBR, EPR, and all that jazz
http://www.aps.org/units/gqi/newsletters/upload/vol6num3.pdf

The PBR Argument - a simplified presentation
http://astairs.posterous.com/the-pbr-argument-a-simplified-presentation

Useful Blogs:
Can the quantum state be interpreted statistically?
http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/

Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/

Philosophical papers:
Statistical-Realism versus Wave-Realism in the Foundations of Quantum
Mechanics

http://philsci-archive.pitt.edu/902...m_in_the_Foundations_of_Quantum_Mechanics.pdf
 
  • #500
Thanks for the references/links bohm2. I think that quantum states can be interpreted statistically, ie., that quantum states don't necessarily represent real physical states. But if you think otherwise, then it would be interesting to read your opinion on that.
 
  • #502
tag.
 
  • #503
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  • #504
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  • #505
That Hardy paper was really confusing. A video (May 8/12) from Perimeter Institute by Robert Spekkens discussing PBR but he doesn't seem persuaded to become a psi-ontologist:

This talk will address the question of whether the PBR theorem should be interpreted as lending evidence against the psi-epistemic research program. I will review the evidence in favour of the psi-epistemic approach and describe the pre-existing reasons for thinking that if a quantum state represents knowledge about reality then it is not reality as we know it, i.e., it is not the kind of reality that is posited in the standard hidden variable framework. I will argue that the PBR theorem provides additional clues for "what has to give" in the hidden variable framework rather than providing a reason to retreat from the psi-epistemic position... The connection between the PBR theorem and other no-go results will be discussed. In particular, I will point out how the second assumption of the theorem is an instance of preparation noncontextuality, a property that is known not to be achievable in any ontological model of quantum theory, regardless of the status of separability (though not in the form posited by PBR). I will also consider the connection of PBR to the failure of local causality by considering an experimental scenario which is in a sense a time-inversion of the PBR scenario.
Why I Am Not a Psi-ontologist
http://pirsa.org/displayFlash.php?id=12050021
 
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  • #506
Bohm2, thank you for this info. In particular, I would like to quote a part of a sentence by Spekkens above:
"... the second assumption of the theorem is an instance of preparation noncontextuality, a property that is known not to be achievable in any ontological model of quantum theory ..."
That was exactly my objection too in an early stage of this thread.
 
  • #508
bohm2 said:
An interesting PhD thesis arguing for state realism that also discusses the recent PBR theorem quite a bit. Interesting, that one of the examiners for this thesis is Robert Spekkens:

The case for quantum state realism
http://ir.lib.uwo.ca/cgi/viewcontent.cgi?filename=0&article=1657&context=etd&type=additional

As I interpret quantum state realism: I would say that ANY 2 particles with the same eigenstates are absolutely indistinguishable. They therefore have NO HIDDEN differences. If you accept that, then you would also conclude that the collapse upon measurement absolutely changes the state and does not reveal a pre-existing characteristic. Thus you would reject the idea that it is only our knowledge which is being updated, and this is not Bayesian conditionalization.

I am not saying this is actually the case, just that is how I understand the concept. The author of the cited paper (Tait) discusses some of these ideas in detail.
 
  • #509
bohm2 said:
Generalisations of the recent Pusey-Barrett-Rudolph theorem for statistical models of quantum phenomena
http://xxx.lanl.gov/abs/1111.6304


...For example, the ‘factorisability’ assumption used by PBR can be replaced by a far weaker ‘compatibility’ assumption for the preparations of uncorrelated quantum states...

in agreement with leifer.
 
  • #510
Another paper on PBR:
The analysis of Pusey, Barrett and Rudolph aims to show there can be no objective physical reality which underlies, and is more general than, the state vector. But there appears to be a gap in their reasoning. To show their result, they use entangled states of independent systems. However, no specific experimental arrangement to detect these entangled states has been proposed. Thus their argument as it stands does not fully show there is a detectable conflict between the predictions of quantum mechanics and the existence of an underlying reality. And it is not clear that one can devise the necessary measuring device.
A problem with the Pusey, Barrett, Rudolph analysis of the reality of the quantum state.
http://lanl.arxiv.org/ftp/arxiv/papers/1206/1206.6491.pdf
 
  • #511
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...
 
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  • #512
becoming a trendPhysical 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/95537/psi-epistemic-theories-in-3-or-more-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/qu...e-interpreted-statistically-again/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.
 
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  • #513
Fredrik said:
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.
 
  • #514
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/c...-post-terry-rudolph-on-nature-versus-nurture/
 
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  • #515
...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):

"[url [Broken]"]Distinct Quantum States Can Be Compatible with a Single State of Reality[/URL]
12 October 2012.
Peter G. Lewis, David Jennings, Jonathan Barrett, Terry Rudolph
 
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  • #516
audioloop said:
the latest (this month paper):

"[url [Broken]"]Distinct Quantum States Can Be Compatible with a Single State of Reality[/URL]
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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  • #517
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.
 
  • #518
A recent explanation of the PBR theorem at a level suitable for a general physicist audience is presented here:
https://www.physicsforums.com/blog.php?b=4330 [Broken]
 
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  • #519
Demystifier said:
A recent explanation of the PBR theorem at a level suitable for a general physicist audience is presented here:
https://www.physicsforums.com/blog.php?b=4330 [Broken]

Nicely done presentation!
 
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  • #520
I present a *non-statistical,* realist QM interpretation in my new book:

http://www.cambridge.org/us/knowledge/discountpromotion/?site_locale=en_US&code=L2TIQM

RK
 
  • #521
Demystifier said:
A recent explanation of the PBR theorem at a level suitable for a general physicist audience is presented here:
https://www.physicsforums.com/blog.php?b=4330 [Broken]
Much appreciated!
 
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  • #522
<h2>1. What is the quantum state?</h2><p>The quantum state refers to the state of a quantum system, which can be described by a mathematical object known as a wave function. This wave function contains all the information about the system, including its position, momentum, and energy.</p><h2>2. What does it mean that the quantum state cannot be interpreted statistically?</h2><p>This means that the behavior of a quantum system cannot be predicted with certainty, as is the case with classical systems. Instead, the quantum state can only be described probabilistically, meaning that we can only calculate the likelihood of a particular outcome.</p><h2>3. Why can't the quantum state be interpreted statistically?</h2><p>This is a fundamental principle of quantum mechanics known as the uncertainty principle. It states that it is impossible to know both the position and momentum of a particle with absolute certainty. This is due to the wave-like nature of particles at the quantum level.</p><h2>4. How is the quantum state used in quantum computing?</h2><p>In quantum computing, the quantum state is used to represent the state of a quantum computer's qubits. These qubits can exist in multiple states simultaneously, allowing for more complex calculations and faster processing than classical computers.</p><h2>5. What are the implications of the quantum state not being able to be interpreted statistically?</h2><p>This has significant implications for our understanding of the universe and the behavior of particles at the quantum level. It also has practical applications in fields such as quantum computing and quantum cryptography.</p>

1. What is the quantum state?

The quantum state refers to the state of a quantum system, which can be described by a mathematical object known as a wave function. This wave function contains all the information about the system, including its position, momentum, and energy.

2. What does it mean that the quantum state cannot be interpreted statistically?

This means that the behavior of a quantum system cannot be predicted with certainty, as is the case with classical systems. Instead, the quantum state can only be described probabilistically, meaning that we can only calculate the likelihood of a particular outcome.

3. Why can't the quantum state be interpreted statistically?

This is a fundamental principle of quantum mechanics known as the uncertainty principle. It states that it is impossible to know both the position and momentum of a particle with absolute certainty. This is due to the wave-like nature of particles at the quantum level.

4. How is the quantum state used in quantum computing?

In quantum computing, the quantum state is used to represent the state of a quantum computer's qubits. These qubits can exist in multiple states simultaneously, allowing for more complex calculations and faster processing than classical computers.

5. What are the implications of the quantum state not being able to be interpreted statistically?

This has significant implications for our understanding of the universe and the behavior of particles at the quantum level. It also has practical applications in fields such as quantum computing and quantum cryptography.

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