Eur. Phys. J. D 64, 147-153 (2011)
https://doi.org/10.1140/epjd/e2011-20017-4

Regular Article

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

¹ Department of Mathematics, University of California, Irvine, CA 92697-3875, USA
² Department of mathematical sciences, Tsinghua University, Beijing 100084, P.R. China
³ Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor, MI 48109, USA
⁴ Department of Computer Science, Wayne State University, Detroit, MI 48202, USA
⁵ National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, 637616 Singapore, Singapore
⁶ Center for Quantum Technologies, National Univeristy of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
⁷ Institute of Advanced Studies, Nanyang Technological University, 60 Nanyang View, 639673 Singapore, Singapore

^a e-mail: dli@math.tsinghua.edu.cn

Received: 10 January 2011
Received in final form: 23 March 2011
Published online: 27 July 2011

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.