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Skew information-based uncertainty relations for quantum channels

  • Shuangshuang FuEmail author
  • Yuan Sun
  • Shunlong Luo
Article
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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.

Keywords

Uncertainty relation Quantum channel Wigner–Yanase skew information 

Notes

Acknowledgements

This work was supported by the Natural Science Foundation of Beijing, 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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijingPeople’s Republic of China
  2. 2.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingPeople’s Republic of China
  3. 3.School of Mathematical SciencesUniversity of the Chinese Academy of SciencesBeijingPeople’s Republic of China

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