Shot-by-shot estimation of quantum measurement accuracy via quantum Bayesian inference

Ordinarily, quantum-measurement based state discrimination methods use Bayesian inference to determine the maximally likely optical input state out of N possible inputs. Each practical single-shot measurement yields a unique vector of N likelihood values (one per each possible outcome) whose significance is not appreciated. Here we show theoretically and experimentally that measured Bayesian likelihood values are equal to observed probabilities of a successful state discrimination. Thus, the vector of Bayesian likelihoods provides significantly more information about the input state than is available in a typical state discrimination measurement.