Quantum discord of states arising from graphs

Quantum discord of states arising from graphs Quantum discord refers to an important aspect of quantum correlations for bipartite quantum systems. In our earlier works, we have shown that corresponding to every graph (combinatorial) there are quantum states whose properties are reflected in the structure of the corresponding graph. Here, we attempt to develop a graph theoretic study of quantum discord that corresponds to a necessary and sufficient condition of zero quantum discord states which says that the blocks of density matrix corresponding to a zero quantum discord state are normal and commute with each other. These blocks have a one-to-one correspondence with some specific subgraphs of the graph which represents the quantum state. We obtain a number of graph theoretic properties representing normality and commutativity of a set of matrices which are indeed arising from the given graph. Utilizing these properties, we define graph theoretic measures for normality and commutativity that results in a formulation of graph theoretic quantum discord. We identify classes of quantum states with zero discord using the developed formulation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantum discord of states arising from graphs

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
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/s11128-017-1636-5
Publisher site
See Article on Publisher Site

Abstract

Quantum discord refers to an important aspect of quantum correlations for bipartite quantum systems. In our earlier works, we have shown that corresponding to every graph (combinatorial) there are quantum states whose properties are reflected in the structure of the corresponding graph. Here, we attempt to develop a graph theoretic study of quantum discord that corresponds to a necessary and sufficient condition of zero quantum discord states which says that the blocks of density matrix corresponding to a zero quantum discord state are normal and commute with each other. These blocks have a one-to-one correspondence with some specific subgraphs of the graph which represents the quantum state. We obtain a number of graph theoretic properties representing normality and commutativity of a set of matrices which are indeed arising from the given graph. Utilizing these properties, we define graph theoretic measures for normality and commutativity that results in a formulation of graph theoretic quantum discord. We identify classes of quantum states with zero discord using the developed formulation.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jun 17, 2017

References

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