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The uncertainty relation for quantum channels based on skew information

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Abstract

Uncertainty relations are the basis of quantum mechanics. We study the uncertainty relation for quantum channels by skew information. An uncertainty relation for quantum channels is provided, which can be generalized to more than two channels. This uncertainty relation is shown to be independent of the Kraus representations of quantum channels. We then establish an uncertainty relation for skew information of coherence under different bases in qubit systems.

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Acknowledgements

M. J. Zhao is supported by the National Natural Science Foundation of China under Grants No. 12171044. Z. Wang is supported by Shandong Provincial National Natural Science Foundation under Grant No. ZR2020MA034. T. Li is supported by Projection of education and teaching, Beijing Technology and Business University, 2021.

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Authors and Affiliations

  1. School of Science, Beijing Information Science and Technology University, Beijing, 100192, People’s Republic of China

    Nan Zhou & Ming-Jing Zhao

  2. School of Mathematics and Computer Application Technology, Jining University, Qufu, 273155, People’s Republic of China

    Zhen Wang

  3. School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, 100048, People’s Republic of China

    Tao Li

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  1. Nan Zhou
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  2. Ming-Jing Zhao
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  3. Zhen Wang
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  4. Tao Li
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Correspondence to Ming-Jing Zhao.

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Zhou, N., Zhao, MJ., Wang, Z. et al. The uncertainty relation for quantum channels based on skew information. Quantum Inf Process 22, 6 (2023). https://doi.org/10.1007/s11128-022-03760-x

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