General bounds for quantum discord and discord distance

General bounds for quantum discord and discord distance For any bipartite state, how strongly can one subsystem be quantum correlated with another? Using the Koashi–Winter relation, we study the upper bound of purified quantum discord, which is given by the sum of the von Neumann entropy of the unmeasured subsystem and the entanglement of formation shared between the unmeasured subsystem with the environment. In particular, we find that Luo et al.’s conjecture on the quantum correlations and the Lindblad conjecture are true under the condition that the entanglement of formation vanishes. Let the discord distance be defined as the difference between the left discord and the right discord. If the Lindblad conjecture is true, we show that the joint entropy is a tight upper bound for the discord distance. Further, we obtain a necessary and sufficient condition for saturating upper bounds of purified quantum discord and discord distance separately with the equality conditions for the Araki–Lieb inequality and the Lindblad conjecture. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

General bounds for quantum discord and discord distance

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Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-0944-x
Publisher site
See Article on Publisher Site

Abstract

For any bipartite state, how strongly can one subsystem be quantum correlated with another? Using the Koashi–Winter relation, we study the upper bound of purified quantum discord, which is given by the sum of the von Neumann entropy of the unmeasured subsystem and the entanglement of formation shared between the unmeasured subsystem with the environment. In particular, we find that Luo et al.’s conjecture on the quantum correlations and the Lindblad conjecture are true under the condition that the entanglement of formation vanishes. Let the discord distance be defined as the difference between the left discord and the right discord. If the Lindblad conjecture is true, we show that the joint entropy is a tight upper bound for the discord distance. Further, we obtain a necessary and sufficient condition for saturating upper bounds of purified quantum discord and discord distance separately with the equality conditions for the Araki–Lieb inequality and the Lindblad conjecture.

Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 13, 2015

References

  • Experimental distribution of entanglement with separable carriers
    Fedrizzi, A; Zuppardo, M; Gillett, GG; Broome, MA; Almeida, MP; Paternostro, M; White, AG; Paterek, T
  • Quantum discord and remote state preparation
    Giorgi, GL
  • Upper bound and shareability of quantum discord based on entropic uncertainty relations
    Hu, ML; Fan, H

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