# The quantum state can be interpreted statistically, again

Now there are two papers

The quantum state cannot be interpreted statistically

http://arxiv.org/abs/1111.3328

(It was discussed here the consecuences of this "no-go theorem")

And this one (two of the authors are the same as the previous paper):

The quantum state can be interpreted statistically

http://arxiv.org/abs/1201.6554

I would like to note this: titles give only poor information about the content, and they seem even maliciously chosen, but the mere existence of the two papers is funny anyway..

The question is : Which is more general!?

From the paper: "Recently, a no-go theorem was proven [21] showing that a $\psi$-epistemic interpretation is impossible. A key assumption of the argument in [21] is preparation independence situations where quantum theory assigns independent product states are presumed to be completely describable by independently combining the two purportedly deeper descriptions for each system. Here, we will show via explicit constructions that without this assumption, $\psi$-epistemic models can be constructed with all quantum predictions retained"

As I understand the second one just seems more general (because of "less assumptions"), but by no means Newton's dynamics is more general than Einsein's relativity because "it lacks of c=constant assumption". It's weird anyway, because it would mean that if " wavefunction is a real physical object" (a funny phrase from www.nature.com article) would depend on assumptions!, then what kind of realism depend on assumptions?

Perhaps a point to discuss (assuming the theorem is well proven) is whether those assumptions have sense, if they come from experiments, or if they are just limiting the scope (toy model), or if those are random assumtions that have no source.

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@dmckee fixed, thanks –  HDE Feb 8 '12 at 19:12
I think that these discussions don't really belong to a physics forum. All these papers – whether they have "can" or "cannot" in the title – implicitly and sometimes explicitly assume that there is an objective and in this sense classical "model" that underlies the probabilistic predictions. The absence of such a model can't be "proved quite rigorously" which is why additional research about such proofs is a hobby for mathematical nitpickers but the physics observations surely do imply, in the physics sense, that the positivist/Copenhagen/probabilistic/Born interpretation is the only one. –  Luboš Motl Feb 9 '12 at 10:13
@LubošMotl: It can't be proved because there is a counterexample in Bohm, and this is suggestive that perhaps there is a better theory out there. One cannot be certain until one makes it or excludes it with good hypotheses, so these papers are not so ridiculous (although the arguments are not so profound in my opinion, since they don't make a new theory). –  Ron Maimon Sep 14 '12 at 19:46

That goes with the epistemic, ontic or complete interpretations of the quantum state.

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 statement given by you:

"Recently, a no-go theorem was proven showing that a ψ-epistemic interpretation is impossible"

is far from being settled,

Leifer, August 28, 2012.

Maximally epistemic interpretations of the quantum state and contextuality http://arxiv.org/pdf/1208.5132.pdf

......If one could prove, without auxiliary assumptions, that the support of every distribution in an ontological model must contain a set of states that are not shared by the distribution corresponding to any other quantum state, then these results would follow. Whether this can be proved is an important open question...

.

Montina, June 15, 2012

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

...We show that classical simulations employing a ﬁnite amount of communication can be derived from a special class of hidden variable theories where quantum states represent statistical knowledge about the classical state and not an element of reality... ...In this paper, we will show that ψ-epistemic theories have a pivotal role also in quantum communication and can determine an upper bound for the communication complexity of a quantum channel...

.

Spekkens, 10 July 2012

Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction

http://arxiv.org/pdf/1111.5057.pdf

...The success of this model in reproducing aspects of quantum theory provides additional evidence in favour of interpretations of quantum theory where quantum states describe states of incomplete knowledge rather than states of reality...

.

foundational concepts

Spekkens

Einstein, incompleteness, and the epistemic view of quantum states http://arxiv.org/pdf/0706.2661.pdf

...ψ-ontic if every complete physical state or ontic state in the theory is consistent with only one pure quantum state; we call it ψ-epistemic if there exist ontic states that are consistent with more than one pure quantum state...

...The simplest possibility is a one-to-one relation. A schematic of such a model is presented in part (a) of Fig. 1, where we have represented the set of all quantum states by a onedimensional ontic state space Λ labeled by ψ. We refer to such models as ψ-complete because a pure quantum state provides a complete description of reality...

Friederich, 2012.

Interpreting Heisenberg Interpreting Quantum States

http://philsci-archive.pitt.edu/9269/1/heisenbergpaper.pdf

...the view that quantum states are not descriptions of quantum systems but rather reflect the state assigning observers' epistemic relations to these systems...

a conference about New Perspectives on the Quantum State

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Distinct Quantum States Can Be Compatible with a Single State of Reality--prl.aps.org/pdf/PRL/v109/i15/e150404 –  user12103 Oct 12 '12 at 21:00
fantastic answer ++ –  Anno2001 Nov 3 '12 at 10:57

All that the new paper is saying is a long-winded version of the last section of my answer here: Consequences of the new theorem in QM? . There is an implicit assumption in the older paper that the state of two isolated systems is the concatenation of the states of the two systems, and this is not justified in reasonable theories that attempt to reproduce QM from statistics. So the new paper is right, the old paper is not as much of a killer as it pretends to be, but it was on stackexchange before it was on arxiv, and so there's no news here for this site, I think.

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