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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Inequalities for quantum Fisher information
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by Paolo Gibilisco, Daniele Imparato and Tommaso Isola
Proc. Amer. Math. Soc. 137 (2009), 317-327
DOI: https://doi.org/10.1090/S0002-9939-08-09447-1
Published electronically: August 4, 2008

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.
References
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Bibliographic Information
  • Paolo Gibilisco
  • Affiliation: Dipartimento SEFEMEQ, Facoltà di Economia, Università di Roma “Tor Vergata”, Via Columbia 2, 00133 Rome, Italy
  • Email: gibilisco@volterra.uniroma2.it
  • Daniele Imparato
  • Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
  • Email: daniele.imparato@polito.it
  • Tommaso Isola
  • Affiliation: Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Rome, Italy
  • Email: isola@mat.uniroma2.it
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 317-327
  • MSC (2000): Primary 62B10, 94A17; Secondary 46L30, 46L60
  • DOI: https://doi.org/10.1090/S0002-9939-08-09447-1
  • MathSciNet review: 2439456