Disproving the Peres conjecture by showing Bell nonlocality from bound entanglement.

@article{Vrtesi2014DisprovingTP,
  title={Disproving the Peres conjecture by showing Bell nonlocality from bound entanglement.},
  author={Tam{\'a}s V{\'e}rtesi and Nicolas Brunner},
  journal={Nature communications},
  year={2014},
  volume={5},
  pages={
          5297
        }
}
Quantum entanglement has a central role in many areas of physics. To grasp the essence of this phenomenon, it is fundamental to understand how different manifestations of entanglement relate to each other. In 1999, Peres conjectured that Bell nonlocality is equivalent to distillability of entanglement. The intuition of Peres was that the non-classicality of an entangled state, as witnessed via Bell inequality violation, implies that pure entanglement can be distilled from this state, hence… 
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References

SHOWING 1-10 OF 57 REFERENCES
Steering bound entangled States: a counterexample to the stronger Peres conjecture.
TLDR
A method is provided to generate systematically bound entangled quantum states which can still be used for steering and, therefore, to rule out local hidden state models and sheds light on the relations between the various views on quantum correlations.
Quantum nonlocality does not imply entanglement distillability.
TLDR
This work presents analytically a 3-qubit entangled state that is separable along any bipartition, and implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled.
Quantum entanglement
All our former experience with application of quantum theory seems to say that what is predicted by quantum formalism must occur in the laboratory. But the essence of quantum formalism— entanglement,
All bipartite entangled States display some hidden nonlocality.
TLDR
It is demonstrated that a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality can be demonstrated in a certain kind of Bell experiment for all entangled states, and it is proved that for each entangled state sigma, there exists another state rho not violating the CHSH inequality.
Distillability, bell inequalities, and multiparticle bound entanglement.
  • A. Acín
  • Physics
    Physical review letters
  • 2002
TLDR
It is proved that for all the states violating a Bell inequality there exists at least one splitting of the parties into two groups such that some pure-state entanglement can be distilled, obtaining a connection between Bell inequalities and bipartite distillable entanglements.
Entanglement swapping of noisy states: A kind of superadditivity in nonclassicality
We address the question as to whether an entangled state that satisfies local realism will give a violation of the same after entanglement swapping in a suitable scenario. We consider such a
Negativity and steering: A stronger Peres conjecture
The violation of a Bell inequality certifies the presence of entanglement even if neither party trusts their measurement devices. Recently Moroder et al. [T. Moroder, J.-D. Bancal, Y.-C. Liang, M.
Device-independent entanglement quantification and related applications.
TLDR
It is shown that the method presented provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device-independent entanglement witnesses involving an arbitrary number of parties.
Quantum networks reveal quantum nonlocality.
TLDR
This work shows, using its framework, how any one-way entanglement distillable state leads to nonlocal correlations and proves that quantum nonlocality is a non-additive resource, which can be activated.
Genuine hidden quantum nonlocality.
TLDR
This work presents a class of two-qubit entangled states, for which a local model is constructed for the most general local measurements, and shows that the states violate a Bell inequality after local filtering.
...
...