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Sum uncertainty relations based on Wigner–Yanase skew information

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Abstract

We study sum uncertainty relations for arbitrary finite N quantum mechanical observables. Some uncertainty inequalities are presented by using skew information introduced by Wigner and Yanase. These uncertainty inequalities are nontrivial as long as the observables are mutually noncommutative. The relations among these new and existing uncertainty inequalities have been investigated. Detailed examples are presented.

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Acknowledgments

We would like to thank Dr. Shu-Hao Wang for his helpful discussions and suggestions. This work is supported by the National Basic Research Program of China (2015CB921002), the National Natural Science Foundation of China Grant Nos. 11175094, 91221205, and 11275131.

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Authors and Affiliations

  1. State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, 100084, China

    Bin Chen & Gui-Lu Long

  2. Tsinghua National Laboratory for Information Science and Technology, Beijing, 100084, China

    Bin Chen & Gui-Lu Long

  3. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shao-Ming Fei

  4. Max-Planck-Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    Shao-Ming Fei

  5. Collaborative Innovation Center of Quantum Matter, Beijing, 100084, China

    Gui-Lu Long

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  1. Bin Chen
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  2. Shao-Ming Fei
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  3. Gui-Lu Long
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Correspondence to Bin Chen.

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Chen, B., Fei, SM. & Long, GL. Sum uncertainty relations based on Wigner–Yanase skew information. Quantum Inf Process 15, 2639–2648 (2016). https://doi.org/10.1007/s11128-016-1274-3

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  • DOI: https://doi.org/10.1007/s11128-016-1274-3

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