Sum uncertainty relations based on metric-adjusted skew information

Abstract

We show that the sum uncertainty relations for Wigner–Yanase skew information introduced in Chen et al. (Quantum Inf Process 15:2639–2648, 2016) can hold for an arbitrary metric adjusted skew information. A refinement of one main result in that paper is formulated via a series of lower bounds consisting of the skew information of any prescribed size of the combinations. We also study the metric-adjusted skew information-based uncertainty relations for quantum channels in the spirit of Fu et al. (Quantum Inf Process 18:258, 2019).

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (11301025).

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Correspondence to Liang Cai.

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Cai, L. Sum uncertainty relations based on metric-adjusted skew information. Quantum Inf Process 20, 72 (2021). https://doi.org/10.1007/s11128-021-03008-0

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Keywords

  • Metric-adjusted skew information
  • Regular operator monotone function
  • Sum uncertainty relation
  • Hlawka’s inequality
  • Quantum channel

Mathematics Subject Classification

  • 94A17
  • 81P15
  • 15A45