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Averaged Wigner-Yanase-Dyson information as a quantum uncertainty measure

  • X. Li
  • D. LiEmail author
  • H. Huang
  • X. Li
  • L. C. Kwek
Regular Article Quantum Information

Abstract

The average of the skew information over the observables was proposed by Luo as a quantum uncertainty measure. In this paper, we investigate the interesting properties of Wigner-Yanase-Dyson (WYD) information, which is a generalization of skew information. Then, by averaging WYD information over the observables we propose a general quantum uncertainty measure of mixed states, and study the properties of the measure. Note that the general quantum uncertainty measure depends on the parameter α and reduces to Luo’s measure when α is equal to 1/2. To get rid of the parameter α, we propose the average of the general measure over the parameter α as a quantum uncertainty measure of mixed states and discuss its properties. The two measures can be considered as the intrinsic properties of mixed state. The construction is reminiscent of the generalized entropies that have shown to be useful in many applications.

Keywords

Entropy Mixed State Pure State Generalize Entropy Unitary Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA
  2. 2.Department of mathematical sciencesTsinghua UniversityBeijingP.R. China
  3. 3.Electrical Engineering and Computer Science DepartmentUniversity of MichiganAnn ArborUSA
  4. 4.Department of Computer ScienceWayne State UniversityDetroitUSA
  5. 5.National Institute of EducationNanyang Technological UniversitySingaporeSingapore
  6. 6.Center for Quantum TechnologiesNational Univeristy of SingaporeSingaporeSingapore
  7. 7.Institute of Advanced StudiesNanyang Technological UniversitySingaporeSingapore

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