Quantum state estimation and large deviations

P. Blanchard, Ph. Combe, M. Sirugue +1 more

Masahito Hayashi

F. De Martini, AND SCIARRINO F., MARCO RICCI

Izumi Ojima, Kazuya Okamura

In the earlier paper [1], we have proposed the large deviation strategy (LDS) and discussed its first level. By efficient use of the central measure, we will establish a quantum version of Sanov's theorem, the Bayesian escort predictive state and the widely applicable information criteria for quantum states in LDS second level. Finally, these results are re-examined in the context of quantum estimation theory, and organized as quantum model selection, i.e., a quantum version of model selection.

Michael Keyl

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 pure states and 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 → ∞), analyze its large deviation behavior, and calculate explicitly the corresponding rate function which describes the exponential decrease of error probabilities in the limit N → ∞. Finally, we discuss the question whether the proposed scheme provides the fastest possible decay of error probabilities.