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arXiv:math-ph/0702058

Inequalities for quantum Fisher information

Paolo Gibilisco, Daniele Imparato, Tommaso Isola

Published Feb 16, 2007• 0 citations
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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.

DOI
10.48550/arxiv.math-ph/0702058

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An inequality relating the Wigner-Yanase information and the SLDSLDSLD-quantum Fisher information was established by Luo (
We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum uncertainty quantity excluding the classical mixture. And we introduce a generalized Fisher information and then derive a generalized Cramer-Rao inequality. We also give an example for our generalized Fisher information and then derive the uncertainty relation for two observables.
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