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Soft Computing

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20-02-2017 | Focus

Extrapolated quantum states, void states and a huge novel class of distillable entangled states

Authors: Michel Boyer, Aharon Brodutch, Tal Mor

Published in: Soft Computing | Issue 19/2017

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Abstract

A nice and interesting property of any pure tensor product state is that each such state has distillable entangled states at an arbitrarily small distance \(\epsilon \) in its neighborhood. We say that such nearby states are \(\epsilon \)-entangled, and we call the tensor product state in that case, a “boundary separable state,” as there is entanglement at any distance from this “boundary.” Here we find a huge class of separable states that also share the property mentioned above—they all have \(\epsilon \)-entangled states at any small distance in their neighborhood. Furthermore, the entanglement they have is proved to be distillable. We then extend this result to the discordant/classical cut and show that all classical states (correlated and uncorrelated) have discordant states at distance \(\epsilon \), and provide a constructive method for finding \(\epsilon \)-discordant states.

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A preliminary version of this work (without discordant states) appeared in TPNC-2014 (Boyer and Mor 2014).

The term product basis should not be confused with the classical basis of Groisman et al. (2007) which is a product of local bases, rather than a basis of product states.

Note that a separable \(N-1\)-void state is a tensor product state.

The term classical is used in a variety of ways in the literature; here, we use it in the sense of correlations as in Modi et al. (2012).

Although the Peres criterion is well known, it is provided for completeness of the exposition in Appendix 8.

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Title: Extrapolated quantum states, void states and a huge novel class of distillable entangled states
Authors: Michel Boyer
Aharon Brodutch
Tal Mor
Publication date: 20-02-2017
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 19/2017
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-017-2518-6

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