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A Generalized Uncertainty Relation

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Abstract

By using a generalization of the Wigner-Yanase-Dyson skew information, a quantity \(|U_{\rho }^{\alpha }|(A)\) is introduced in this paper for every Hilbert-Schmidt operator A on a Hilbert space H and a related uncertainty relation was established. The obtained inequality generalizes a known uncertainty relation. Moreover, a negative answer to a conjecture induced in Dou and Du (Int. J. Theor. Phys. 53, 952–958, 2014) was given by a counterexample.

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Acknowledgments

The author would like to thank Prof. Hong-Ke Du and Prof. Huai-Xin Cao for their guidance, encouragement and for all the time they spent on. In addition, the author would like to thank anonymous referees for his/her valuable comments and suggestions which helped to improve the presentation of this paper.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, People’s Republic of China

    Zhengli Chen, Lili Liang, Haojing Li & Wenhua Wang

Authors
  1. Zhengli Chen
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  2. Lili Liang
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  3. Haojing Li
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  4. Wenhua Wang
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Corresponding author

Correspondence to Zhengli Chen.

Additional information

This research was partially supported by the National Natural Science Foundation of China(No.11371012), the IFGP of Shaanxi Normal University (No.2013CXB012) and the FRF for the Central Universities (GK 201002006).

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Chen, Z., Liang, L., Li, H. et al. A Generalized Uncertainty Relation. Int J Theor Phys 54, 2644–2651 (2015). https://doi.org/10.1007/s10773-014-2496-8

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  • DOI: https://doi.org/10.1007/s10773-014-2496-8

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