Secure Key from Bound Entanglement

Karol Horodecki, Michał Horodecki, Paweł Horodecki, and Jonathan Oppenheim
Phys. Rev. Lett. 94, 160502 – Published 26 April 2005

Abstract

We characterize the set of shared quantum states which contain a cryptographically private key. This allows us to recast the theory of privacy as a paradigm closely related to that used in entanglement manipulation. It is shown that one can distill an arbitrarily secure key from bound entangled states. There are also states that have less distillable private keys than the entanglement cost of the state. In general, the amount of distillable key is bounded from above by the relative entropy of entanglement. Relationships between distillability and distinguishability are found for a class of states which have Bell states correlated to separable hiding states. We also describe a technique for finding states exhibiting irreversibility in entanglement distillation.

  • Received 13 September 2003

DOI:https://doi.org/10.1103/PhysRevLett.94.160502

©2005 American Physical Society

Authors & Affiliations

Karol Horodecki1, Michał Horodecki2, Paweł Horodecki3, and Jonathan Oppenheim2,4,5

  • 1Department of Mathematics, Physics and Computer Science, University of Gdańsk, Poland
  • 2Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Poland
  • 3Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, 80-952 Gdańsk, Poland
  • 4Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom
  • 5Racah Institute of Theoretical Physics, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel

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Issue

Vol. 94, Iss. 16 — 29 April 2005

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