Berlin 2005 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 9: Quantum Information Theory

MP 9.1: Fachvortrag

Wednesday, March 9, 2005, 14:00–14:20, TU MA141

Quantum state estimation and large deviations — •Michael Keyl — Univ. Pavia, QUIT Group, Dipartimento Di Fisica “A. Volta”, via Bassi 6, I-27100 Pavia, Italy

In this paper we propose a method to estimate the density matrix ρ of a d-level quantum system by measurements on the N-fold system in the joint state ρ^{⊗ N}. 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 ρ. We show that it is consistent (i.e. the original input state ρ is recovered with certainty if N → ∞) and analyze its large deviation behavior. In addition we calculate explicitly the corresponding rate function which describes the exponential decrease of error probabilities in the limit N → ∞. For pure input states, or if ρ is mixed but only information about its spectrum is required, we then show that the proposed scheme is optimal in the sense that it provides the fastest possible decay of error probabilities. In the general case, however, the optimality question remains open.