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August 2004 Maximum Fisher information in mixed state quantum systems
Alessandra Luati
Ann. Statist. 32(4): 1770-1779 (August 2004). DOI: 10.1214/009053604000000436


We deal with the maximization of classical Fisher information in a quantum system depending on an unknown parameter. This problem has been raised by physicists, who defined [Helstrom (1967) Phys. Lett. A 25 101–102] a quantum counterpart of classical Fisher information, which has been found to constitute an upper bound for classical information itself [Braunstein and Caves (1994) Phys. Rev. Lett. 72 3439–3443]. It has then become of relevant interest among statisticians, who investigated the relations between classical and quantum information and derived a condition for equality in the particular case of two-dimensional pure state systems [Barndorff-Nielsen and Gill (2000) J. Phys. A 33 4481–4490].

In this paper we show that this condition holds even in the more general setting of two-dimensional mixed state systems. We also derive the expression of the maximum Fisher information achievable and its relation with that attainable in pure states.


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Alessandra Luati. "Maximum Fisher information in mixed state quantum systems." Ann. Statist. 32 (4) 1770 - 1779, August 2004.


Published: August 2004
First available in Project Euclid: 4 August 2004

zbMATH: 1045.62122
MathSciNet: MR2089142
Digital Object Identifier: 10.1214/009053604000000436

Primary: 62B05
Secondary: 62F10

Keywords: Fisher information , Helstrom information , mixed states , Parametric quantum models , pure states , symmetric logarithmic derivatives

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 4 • August 2004
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