A multipartite entanglement measure based on coefficient matrices

A multipartite entanglement measure based on coefficient matrices The quantification of quantum entanglement has been extensively studied in past years. However, many existing entanglement measures are difficult to calculate. And lots of them are introduced only for bipartite system or only for the systems constituted by qubits. In this paper, we propose an entanglement measure for multipartite system based on vector lengths and the angles between vectors of the coefficient matrices. Our entanglement measure is simple and feasible, with a remarkable geometric meaning. Furthermore, we prove that our entanglement measure satisfies the three necessary conditions which are required for any entanglement measure: (1) It vanishes if and only if the state is (fully) separable; (2) it remains invariant under local unitary transformations; and (3) it cannot increase under local operation and classical communication. Finally, we apply our entanglement measure on some computational examples. It demonstrates that our entanglement measure is capable of dealing with quantum pure states with arbitrary dimensions and parties. Meanwhile, because it only needs to compute the vector lengths and the angles between vectors of every bipartition coefficient matrix, our entanglement measure is easy to calculate. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

A multipartite entanglement measure based on coefficient matrices

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Publisher
Springer US
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/s11128-015-1023-z
Publisher site
See Article on Publisher Site

Abstract

The quantification of quantum entanglement has been extensively studied in past years. However, many existing entanglement measures are difficult to calculate. And lots of them are introduced only for bipartite system or only for the systems constituted by qubits. In this paper, we propose an entanglement measure for multipartite system based on vector lengths and the angles between vectors of the coefficient matrices. Our entanglement measure is simple and feasible, with a remarkable geometric meaning. Furthermore, we prove that our entanglement measure satisfies the three necessary conditions which are required for any entanglement measure: (1) It vanishes if and only if the state is (fully) separable; (2) it remains invariant under local unitary transformations; and (3) it cannot increase under local operation and classical communication. Finally, we apply our entanglement measure on some computational examples. It demonstrates that our entanglement measure is capable of dealing with quantum pure states with arbitrary dimensions and parties. Meanwhile, because it only needs to compute the vector lengths and the angles between vectors of every bipartition coefficient matrix, our entanglement measure is easy to calculate.

Journal

Quantum Information ProcessingSpringer Journals

Published: May 16, 2015

References

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