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Quantum Information Processing

, Volume 14, Issue 8, pp 2861–2881 | Cite as

A multipartite entanglement measure based on coefficient matrices

  • Chao Zhao
  • Guo-wu Yang
  • William N. N. Hung
  • Xiao-yu Li
Article

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.

Keywords

Multipartite entanglement Entanglement measure Coefficient matrices 

Notes

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 61272175.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Chao Zhao
    • 1
  • Guo-wu Yang
    • 1
  • William N. N. Hung
    • 2
  • Xiao-yu Li
    • 3
  1. 1.Big Data Research CenterUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.Synopsys Inc.Mountain ViewUSA
  3. 3.School of Information and Software EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina

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