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Non-Hermitian extensions of uncertainty relations with generalized metric adjusted skew information

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Abstract

In quantum mechanics, it is well known that the Heisenberg–Schrödinger uncertainty relations hold for two non-commutative observables and density operator. Recently some people start to focus on the uncertainty relations for two non-commutative non-Hermitian operators and density operator. In this paper, we introduce the generalized metric adjusted skew information, generalized metric adjusted correlation measure and the related quantities for non-Hermitian operators. Various properties of them are discussed. Finally, we establish several generalizations of uncertainty relation expressed in terms of the generalized metric adjusted skew information and obtain several results including previous results which can be given as corollaries of our non-Hermitian extensions of Heisenberg-type or Schrödinger-type uncertainty relations.

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Acknowledgements

This subject was supported by the NNSF of China (Nos. 11701011, 61463001, 11761001, 11761003), the NSF of Ningxia (Nos. 2018AAC03106,2018AAC03107), the SRP for North Minzu University (Nos. 2017SXKY02, 2017KJ34), the First-Class Disciplines Foundation of Ningxia(No.NXYLXK2017B09), Ningxia Key Laboratory of Intelligent Information and Big Data Processing.

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Authors and Affiliations

  1. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China

    Yajing Fan

  2. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Huaixin Cao

  3. School of Ethnic Education, Shaanxi Normal University, Xi’an, 710062, China

    Wenhua Wang

  4. Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin, 300071, China

    Huixian Meng

  5. Department of Mathematics, Changji College, Changji, 831100, China

    Liang Chen

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  1. Yajing Fan
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  2. Huaixin Cao
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  3. Wenhua Wang
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  4. Huixian Meng
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  5. Liang Chen
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Correspondence to Yajing Fan.

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Fan, Y., Cao, H., Wang, W. et al. Non-Hermitian extensions of uncertainty relations with generalized metric adjusted skew information. Quantum Inf Process 18, 309 (2019). https://doi.org/10.1007/s11128-019-2415-2

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