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Inequalities for quantum Fisher information

Authors: Paolo Gibilisco, Daniele Imparato and Tommaso Isola
Journal: Proc. Amer. Math. Soc. 137 (2009), 317-327
MSC (2000): Primary 62B10, 94A17; Secondary 46L30, 46L60
Published electronically: August 4, 2008
MathSciNet review: 2439456
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Abstract: An inequality relating the Wigner-Yanase information and the $ SLD$-quantum Fisher information was established by Luo (Proc. Amer. Math. Soc., 132, pp. 885-890, 2004). In this paper, we generalize Luo's inequality to any regular quantum Fisher information. Moreover, we show that this general inequality can be derived from the Kubo-Ando inequality, which states that any matrix mean is greater than the harmonic mean and smaller than the arithmetic mean.

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Additional Information

Paolo Gibilisco
Affiliation: Dipartimento SEFEMEQ, Facoltà di Economia, Università di Roma “Tor Vergata”, Via Columbia 2, 00133 Rome, Italy

Daniele Imparato
Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy

Tommaso Isola
Affiliation: Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Rome, Italy

Keywords: Fisher information, operator monotone functions, matrix means, quantum Fisher information
Received by editor(s): February 16, 2007
Received by editor(s) in revised form: December 10, 2007
Published electronically: August 4, 2008
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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