2016/05/31 by The Tien Mai, Pierre Alquier · 1 citation
Mathematics · Physics and Astronomy · #math.ST #math-ph #math.MP #quant-ph #stat.TH
paper · pdf · doi:10.1016/j.jspi.2016.11.003
arxiv created 2016/10/10 · arxiv updated 2017/06/15
Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the good and reliable choice in estimating quantum states~\citeblume2010optimal. Several numerical works showed that Bayesian estimations are comparable to, and even better than other methods in the problem of 1-qubit state recovery. However, the problem of choosing prior distribution in the general case of n qubits is not straightforward. More importantly, the statistical performance of Bayesian type estimators have not been studied from a theoretical perspective yet. In this paper, we propose a novel prior for quantum states (density matrices), and we define pseudo-Bayesian estimators of the density matrix. Then, using PAC-Bayesian theorems, we derive rates of convergence for the posterior mean. The numerical performance of these estimators are tested on simulated and real datasets.