Optimal, reliable estimation of quantum states

Abstract

Accurately inferring the state of a quantum device from the results of\nmeasurements is a crucial task in building quantum information processing\nhardware. The predominant state estimation procedure, maximum likelihood\nestimation (MLE), generally reports an estimate with zero eigenvalues. These\ncannot be justified. Furthermore, the MLE estimate is incompatible with error\nbars, so conclusions drawn from it are suspect. I propose an alternative\nprocedure, Bayesian mean estimation (BME). BME never yields zero eigenvalues,\nits eigenvalues provide a bound on their own uncertainties, and it is the most\naccurate procedure possible. I show how to implement BME numerically, and how\nto obtain natural error bars that are compatible with the estimate. Finally, I\nbriefly discuss the differences between Bayesian and frequentist estimation\ntechniques.\n