Quantum state estimation and large deviations

Details Quantum state estimation and large deviations Quantum state estimation and large deviations

2004-12-07

arxiv.org/abs/quant-ph/0412053v2

Reviews in Mathematical Physics, Vol. 18, No. 1 (2006) 19-60

Physics

Quantum Physics

LaTex2e, 40 pages, 2 figures. Substantial changes in Section 4: one new subsection (4.1) and another (4.2 was 4.1 in the previ

Scientific paper

10.1142/S0129055X06002565

In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends previous results concerning the estimation of the spectrum of \rho. We show that it is consistent (i.e. the original input state \rho is recovered with certainty if N \to \infty), analyze its large deviation behavior, and calculate explicitly the corresponding rate function which describes the exponential decrease of error probabilities in the limit N \to \infty. Finally we discuss the question whether the proposed scheme provides the fastest possible decay of error probabilities.

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