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].
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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.
@article{1091626187,
author = {Luati, Alessandra},
title = {Maximum Fisher information in mixed state quantum systems},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 1770-1779},
language = {en},
url = {http://dml.mathdoc.fr/item/1091626187}
}
Luati, Alessandra. Maximum Fisher information in mixed state quantum systems. Ann. Statist., Tome 32 (2004) no. 1, pp. 1770-1779. http://gdmltest.u-ga.fr/item/1091626187/