Quantum Information Processing

, Volume 13, Issue 7, pp 1583–1594 | Cite as

Quantum discord of ensemble of quantum states

  • Yao Yao
  • Jing-Zheng Huang
  • Xu-Bo Zou
  • Zheng-Fu Han


We highlight an information-theoretic meaning of quantum discord as the gap between the accessible information and the Holevo bound in the framework of ensemble of quantum states. This complementary relationship implies that a large amount of preexisting arguments about the evaluation of quantum discord can be directly applied to the accessible information and vice versa. For an ensemble of two pure qubit states, we show that one can avoid the optimization problem with the help of the Koashi–Winter relation. Further, for the general case (two mixed qubit states), we recover the main results presented by Fuchs and Caves (Phys Rev Lett 73:3047, 1994), but totally from the perspective of quantum discord. Following this line of thought, we also investigate the geometric discord as an indicator of quantumness of ensembles in detail. Finally, we give an example to elucidate the difference between quantum discord and geometric discord with respect to optimal measurement strategies.


Quantum ensembles Quantum discord Geometric discord  Classically accessible information 



Y. Yao wishes to thank Prof. Shunlong Luo for his helpful comments and valuable suggestions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11121403, 10935010 and 11074261) and the National 973 Program (Grant Nos. 2012CB922104 and 2014CB921402).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Yao Yao
    • 1
    • 2
  • Jing-Zheng Huang
    • 2
  • Xu-Bo Zou
    • 2
  • Zheng-Fu Han
    • 2
  1. 1.Beijing Computational Science Research CenterBeijingChina
  2. 2.Key Laboratory of Quantum InformationUniversity of Science and Technology of ChinaHefei China

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