Annals of Statistics
- Ann. Statist.
- Volume 32, Number 4 (2004), 1770-1779.
Maximum Fisher information in mixed state quantum systems
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.
Ann. Statist., Volume 32, Number 4 (2004), 1770-1779.
First available in Project Euclid: 4 August 2004
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Luati, Alessandra. Maximum Fisher information in mixed state quantum systems. Ann. Statist. 32 (2004), no. 4, 1770--1779. doi:10.1214/009053604000000436. https://projecteuclid.org/euclid.aos/1091626187