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I have recently seen some presentation slides of Michał Horodecki (slide number 77) in which he discussed the following conjecture.

Bound entangled states satisfy all Bell inequalities

The conjecture is not true for multi-partite systems, and the references are given in the talk itself. I believe by now, the bipartite case is also settled, one way or the other.

Bell theorem has some applications in computer science areas, like cryptography (non-local games). Is there some similar application of the (falsification of) the above conjecture? I mean, what are the interesting applications which can take place by disproving the above conjecture? Advanced thanks for any help/suggestions.

To the Moderators: I do not know, whether I should have asked this question in Physics or in Cstheory. Considering the fact that there can be physical applications also, I am posted the question here. Please suggest and/or take the required actions.

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    $\begingroup$ The original paper by Peres is here $\endgroup$ – Trimok Jul 8 '13 at 8:02
  • $\begingroup$ @Trimok thanks a lot for the reference. i missed this paper. do you know the status of the bipartite case (of the above problem)? i could not find it out by tracking the citations of various papers on that problem. $\endgroup$ – RSG Jul 8 '13 at 9:42
  • $\begingroup$ I have used these keywords for web research "Bound entangled states satisfy all Bell inequalities peres" $\endgroup$ – Trimok Jul 8 '13 at 9:49
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    $\begingroup$ You could look at this paper: All Bipartite Entangled States Display Some Hidden Nonlocality. In it's discussion of previous work, it also has a number of references which I think address the question. $\endgroup$ – Peter Shor Jul 8 '13 at 13:33
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This very recent paper: Negativity and steering: a stronger Peres conjecture makes a stronger version of Peres's original conjecture, which would appear to imply that the conjecture is still open.

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For posterity's sake, complimenting Peter's accepted answer, it appears that in a recent paper on the arXiv submitted on 5/01/14, the stronger Peres conjecture was shown to be false : Steering bound entangled states: A counterexample to the stronger Peres conjecture

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