Soft Computing

, Volume 21, Issue 19, pp 5543–5556 | Cite as

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

  • Michel Boyer
  • Aharon BrodutchEmail author
  • Tal Mor


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.


Quantum computing and quantum information Entanglement Distillability Discord 



We thank Lin Chen for helpful comments on the pre-print. MB was partly supported by NSERC and FCAR through INTRIQ. AB was partly supported by NSERC, Industry Canada and CIFAR. TM was partly supported by the Israeli MOD. AB and TM were partly supported The Gerald Schwartz and Heather Reisman Foundation. AB is currently at the Center for Quantum Information and Quantum Control at the University of Toronto.

Compliance with ethical standards

Conflict of interest

The a authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.DIROUniversité de MontréalMontrealCanada
  2. 2.Department of Physics and Astronomy and Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  3. 3.Computer Science DepartmentTechnionHaifaIsrael

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