Quantifying nonclassicality of correlations based on the concept of nondisruptive local state identification

Quantifying nonclassicality of correlations based on the concept of nondisruptive local state... A bipartite state is classical with respect to party A if and only if party A can perform nondisruptive local state identification (NDLID) by a projective measurement. Motivated by this we introduce a class of quantum correlation measures for an arbitrary bipartite state. The measures utilize the general Schatten p-norm to quantify the amount of departure from the necessary and sufficient condition of classicality of correlations provided by the concept of NDLID. We show that for the case of Hilbert–Schmidt norm, i.e., $$p=2$$ p = 2 , a closed formula is available for an arbitrary bipartite state. The reliability of the proposed measures is checked from the information-theoretic perspective. Also, the monotonicity behavior of these measures under LOCC is exemplified. The results reveal that for the general pure bipartite states these measures have an upper bound which is an entanglement monotone in its own right. This enables us to introduce a new measure of entanglement, for a general bipartite state, by convex roof construction. Some examples and comparison with other quantum correlation measures are also provided. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantifying nonclassicality of correlations based on the concept of nondisruptive local state identification

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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/s11128-015-1213-8
Publisher site
See Article on Publisher Site

Abstract

A bipartite state is classical with respect to party A if and only if party A can perform nondisruptive local state identification (NDLID) by a projective measurement. Motivated by this we introduce a class of quantum correlation measures for an arbitrary bipartite state. The measures utilize the general Schatten p-norm to quantify the amount of departure from the necessary and sufficient condition of classicality of correlations provided by the concept of NDLID. We show that for the case of Hilbert–Schmidt norm, i.e., $$p=2$$ p = 2 , a closed formula is available for an arbitrary bipartite state. The reliability of the proposed measures is checked from the information-theoretic perspective. Also, the monotonicity behavior of these measures under LOCC is exemplified. The results reveal that for the general pure bipartite states these measures have an upper bound which is an entanglement monotone in its own right. This enables us to introduce a new measure of entanglement, for a general bipartite state, by convex roof construction. Some examples and comparison with other quantum correlation measures are also provided.

Journal

Quantum Information ProcessingSpringer Journals

Published: Dec 23, 2015

References

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