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.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.

arXiv:math-ph/0702058Feb 16, 20070 citations

An inequality relating the Wigner-Yanase information and the

SLD

-quantum Fisher information was established by Luo (

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.