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The uncertainty of quantum channels in terms of variance

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Abstract

By use of the generalized variance for any operator (not necessarily Hermitian), we introduce the uncertainty of quantum channels as the sum of the generalized variances for the Kraus operators of quantum channels and prove that it satisfies several desirable properties. Then, we establish two trade-off relations between the uncertainty of quantum channels and the entanglement fidelity which is introduced by Schumacher (Phys. Rev. A 54: 2614, 1996) and quantifies how well the channel preserves the entanglement between the input system and the auxiliary system for purification. Finally, we illustrate the uncertainty of quantum channels through some typical examples.

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Acknowledgements

This work was supported by the Young Scientists Fund of the National Natural Science Foundation of China, Grant No. 12005104, the Youth Innovation Promotion Association of CAS, Grant No. 2020002, the National Natural Science Foundation of China, Grant Nos. 11775298 and 61833010, the National Center for Mathematics and Interdisciplinary Sciences, CAS, Grant No. Y029152K51, the Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences, Grant No. 2008DP173182.

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Authors and Affiliations

  1. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, People’s Republic of China

    Yuan Sun

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Nan Li

  3. School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China

    Nan Li

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  1. Yuan Sun
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  2. Nan Li
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Correspondence to Yuan Sun.

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Sun, Y., Li, N. The uncertainty of quantum channels in terms of variance. Quantum Inf Process 20, 25 (2021). https://doi.org/10.1007/s11128-020-02972-3

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