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Inequalities for quantum Fisher information

Paolo Gibilisco·Daniele Imparato·Tommaso Isola
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Abstract

In 2003 Luo proved an inequality relating the Wigner-Yanase information and the $SLD$-information. In this paper we prove that Luo's inequality is a particular case of a general inequality which holds for any regular quantum Fisher information. Moreover we show that this general inequality is a consequence of the Kubo-Ando inequality that states that any matrix mean is bigger than the harmonic mean and smaller than the arithmetic mean.

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Paolo Gibilisco, Daniele Imparato, Tommaso Isola. 2007-02-16. Inequalities for quantum Fisher information. https://arxiv.org/abs/math-ph/0702058

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