Local asymptotic equivalence for quantum models

Cristina Butucea (Université Marne-la-Vallée)
Wednesday, May 3, 2017 - 10:00am
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Quantum statistics is concerned with inference for physical systems described by quantum mechanics. After an introduction to the main notions of quantum statistics: quantum states, measurements, channels, we describe nonparametric quantum models. We prove the local asymptotic equivalence (LAE) of i.i.d. quantum pure states and a quantum Gaussian state, in the sense of Le Cam theory. As an application, we show the optimal rates for the estimation of pure states, for the estimation of some quadratic functionals and for the testing of pure states. Surprisingly, a sharp parametric testing rate is obtained in a nonparametric quantum setup. Joint work with M. Guta and M. Nussbaum.