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Bull. Korean Math. Soc. 2021; 58(1): 59-70

Online first article December 28, 2020      Printed January 31, 2021

https://doi.org/10.4134/BKMS.b191089

Copyright © The Korean Mathematical Society.

Inequalities of operator valued quantum skew information

Byoung Jin Choi, Mi Ra Lee

Jeju National University; Chungbuk National University

Abstract

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In this paper, we study two operator-valued inequalities for quantum Wigner-Yanase-Dyson skew information related to module operators. These are extended results of the trace inequalities for Wigner-Yanase-Dyson skew information. Moreover, we study a sufficient condition to prove an uncertainty relation for operator-valued generalized quantum Wigner-Yanase-Dyson skew information related to module operators and a pair of functions $(f, g)$. Also, we obtain several previous results of scalar-valued cases as a consequence of our main result.

Keywords: Uncertainty relation, Wigner-Yanase-Dyson skew information, module operator

MSC numbers: Primary 94A17, 81P45

Supported by: The first author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2020R1C1C1A01003305)

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