Inequalities for quantum Fisher information

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.

10 pages

References in corpus (2)

• Metric adjusted skew information
• Wigner-Yanase information on quantum state space:the geometric approach

Cited by in corpus (2)

• A Robertson-type Uncertainty Principle and Quantum Fisher Information
• Uncertainty principle for Wigner-Yanase-Dyson information in semifinite von Neumann algebras