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Average entropy of a subsystem over a global unitary orbit of a mixed bipartite state

  • Lin ZhangEmail author
  • Hua Xiang
Article

Abstract

We investigate the average entropy of a subsystem within a global unitary orbit of a given mixed bipartite state in the finite-dimensional space. Without working out the closed-form expression of such average entropy for the mixed state case, we provide an analytical lower bound for this average entropy. In deriving this analytical lower bound, we get some useful by-products of independent interest. We also apply these results to estimate average correlation along a global unitary orbit of a given mixed bipartite state. When the notion of von Neumann entropy is replaced by linear entropy, the similar problem can be considered also, and moreover the exact average linear entropy formula is derived for a subsystem over a global unitary orbit of a mixed bipartite state.

Keywords

Quantum state Unitary orbit Average entropy Average correlation Page’s formula 

Notes

Acknowledgements

L. Zhang is supported by Natural Science Foundation of Zhejiang Province of China (LY17A010027) and also by National Natural Science Foundation of China (Nos.11301124 and 61673145). H. Xiang is supported by the National Natural Science Foundation of China (Nos.11571265 and 11471253). Michael Walter is also acknowledged for his comments on this manuscript.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institute of MathematicsHangzhou Dianzi UniversityHangzhouChina
  2. 2.School of Mathematics and StatisticsWuhan UniversityWuhanChina

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