Inequalities for quantum Fisher information

Gibilisco, Paolo; Imparato, Daniele; Isola, Tommaso

doi:10.1090/S0002-9939-08-09447-1

Inequalities for quantum Fisher information
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by Paolo Gibilisco, Daniele Imparato and Tommaso Isola PDF

Proc. Amer. Math. Soc. 137 (2009), 317-327 Request permission

Abstract:

An inequality relating the Wigner-Yanase information and the $SLD$-quantum Fisher information was established by Luo (Proc. Amer. Math. Soc., 132, pp. 885–890, 2004). In this paper, we generalize Luo’s inequality to any regular quantum Fisher information. Moreover, we show that this general inequality can be derived from the Kubo-Ando inequality, which states that any matrix mean is greater than the harmonic mean and smaller than the arithmetic mean.

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