Adaptive Bayesian quantum tomography

In this paper we revisit the problem of optimal design of quantum tomographic experiments. In contrast to previous approaches where an optimal set of measurements is decided in advance of the experiment, we allow for measurements to be adaptively and efficiently reoptimized depending on data collected so far. We develop an adaptive statistical framework based on Bayesian inference and Shannon's information, and demonstrate a significant reduction in the total number of measurements required as compared to nonadaptive methods, including mutually unbiased bases.