Análise do viés em tomografia do estado quântico de máxima verossimilhança

Abstract

Maximum likelihood quantum state tomography yields estimators that are consistent, provided that the likelihood model is correct, but the maximum likelihood estimators may have bias for any nite data set. The bias of an estimator is the di erence between the expected value of the estimate and the true value of the parameter being estimated. This paper investigates bias in the widely used maximum likelihood quantum state tomography. Our goal is to understand how the amount of bias depends on factors such as the purity of the true state, the number of measurements performed, and the number of di erent bases in which the system is measured. For that, we perform numer- ical experiments that simulate optical homodyne tomography under various conditions, perform tomography, and estimate the bias in the purity of the estimated state. We nd that estimates of higher purity states exhibit considerable bias, such that the estimates have lower purity than the true states.