Soft Computing

pp 1–14

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


DOI: 10.1007/s00500-017-2518-6

Cite this article as:
Boyer, M., Brodutch, A. & Mor, T. Soft Comput (2017). doi:10.1007/s00500-017-2518-6


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 

Funding information

Funder NameGrant NumberFunding Note
    Industry Canada
      Canadian Institute for Advanced Research
        Gerald Schwartz and Heather Reisman Foundation
          Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada
            Ministry of Defense

              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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