2004/08/01 by Alessandra Luati · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #math.ST #msc:62B05 #msc:62F10 #stat.TH #stochastic dynamics and bifurcation
paper · pdf · doi:10.1214/009053604000000436
published as Annals of Statistics 2004, Vol. 32, No. 4, 1770-1779 · Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/009053604000000436
openalex publication_date 2004/08/01 · arxiv created 2004/10/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.