Abstract
The most general quantum measurements in quantum mechanics are described by quantum channels (quantum operations), and intrinsic uncertainties emerge from the state–channel interaction. In this paper, we study uncertainty relations for arbitrary quantum channels in terms of generalized skew information, which was introduced by Wigner and Yanase only for Hermitian operators and has recently been generalized to arbitrary operators. We illustrate the uncertainty relations by explicit examples. Specifically, for unitary channels we make a comparison between the new bounds and existing results.
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Acknowledgements
This work was supported by the Natural Science Foundation of Bei**g, China, Grant No. 1174017, the Young Scientists Fund of the National Natural Science Foundation of China, Grant No. 11605006, the Natural Science Foundation of China, Grant No. 11875317, the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Grant No. Y029152K51, and the Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences, Grant No. 2008DP173182.
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Fu, S., Sun, Y. & Luo, S. Skew information-based uncertainty relations for quantum channels. Quantum Inf Process 18, 258 (2019). https://doi.org/10.1007/s11128-019-2371-x
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DOI: https://doi.org/10.1007/s11128-019-2371-x