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Phys. Rev. A 79, 052106 (2009) [4 pages]

Uncertainty relation of mixed states by means of Wigner-Yanase-Dyson information

D. Li,1 X. Li,2 F. Wang,3 H. Huang,4 X. Li,5 and L. C. Kwek6,7,8
1Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
2Department of Mathematics, University of California, Irvine, California 92697-3875, USA
3Insurance Department, Central University of Finance and Economics, Beijing 100081, China
4Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor, Michigan 48109, USA
5Department of Computer Science, Wayne State University, Detroit, Michigan 48202, USA
6National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore
7Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
8Institute of Advanced Studies (IAS), Nanyang Technological University, 60 Nanyang View, Singapore 639673, Singapore

Received 21 February 2009; published 6 May 2009

The variance of an observable in a quantum state is usually used to describe Heisenberg uncertainty relation. For mixed states, the variance includes quantum and classical uncertainties. By means of the skew information and the decomposition of the variance, a stronger uncertainty relation was presented by Luo [ Phys. Rev. A 72, 042110 (2005)]. In this paper, by using Wigner-Yanase-Dyson information which is a generalization of the skew information, we propose a general uncertainty relation of mixed states.

©2009 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevA.79.052106
DOI: 10.1103/PhysRevA.79.052106
PACS: 03.65.Ta
  • 03.65.Ta
    Foundations of quantum mechanics; measurement theory
  • YEAR: 2009
KEYWORDS: Heisenberg model, information theory, measurement theory, quantum theory

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