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

Abstract

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.

Citation

Download Citation

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

Information

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

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

Subjects:
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
Back to Top