Inequalities for quantum Fisher information

The quantum Fisher information (QFI) of certain multipartite entangled quantum states is larger than what is reachable by separable states, providing a metrological advantage. Are these nonclassical correlations strong enough to potentially violate a Bell inequality? Here, we present evidence from two examples. First, we discuss a Bell inequality designed for spin-squeezed states which is violated only by quantum states with a large QFI. Second, we relax a well-known lower bound on the QFI to find the Mermin Bell inequality as a special case. However, a fully general link between QFI and Bell correlations is still open.The quantum Fisher information (QFI) of certain multipartite entangled quantum states is larger than what is reachable by separable states, providing a metrological advantage. Are these nonclassical correlations strong enough to potentially violate a Bell inequality? Here, we present evidence from two examples. First, we discuss a Bell inequality designed for spin-squeezed states which is violated only by quantum states with a large QFI. Second, we relax a well-known lower bound on the QFI to find the Mermin Bell inequality as a special case. However, a fully general link between QFI and Bell correlations is still open.

arXiv:1810.01330Physical Review AApr 17, 201925 citations

Paolo Gibilisco, Daniele Imparato, Tommaso Isola

An inequality relating the Wigner-Yanase information and the $SLD$ -quantum Fisher information was established by Luo (An inequality relating the Wigner-Yanase information and the $SLD$-quantum Fisher information was established by Luo (

Proceedings of the American Mathematical SocietyAug 4, 200837 citations

Inequalities for quantum Fisher information

Paolo Gibilisco, Daniele Imparato, Tommaso Isola

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

Quantum Fisher Information and Uncertainty Relations

Shunlong Luo

Letters in Mathematical PhysicsAug 1, 200094 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.