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Inequalities for quantum Fisher information
Author(s):
Paolo
Gibilisco;
Daniele
Imparato;
Tommaso
Isola
Journal:
Proc. Amer. Math. Soc.
137
(2009),
317-327.
MSC (2000):
Primary 62B10, 94A17;
Secondary 46L30, 46L60
Posted:
August 4, 2008
MathSciNet review:
2439456
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Additional information
Abstract:
An inequality relating the Wigner-Yanase information and the  -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
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
DOI:
10.1090/S0002-9939-08-09447-1
PII:
S 0002-9939(08)09447-1
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
Posted:
August 4, 2008
Communicated by:
Richard C. Bradley
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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