The minimum variance of estimates in quantum signal detection

Abstract

A quantum-mechanical form of the Cramér-Rao inequality is derived, setting a lower bound to the variance of an unbiased estimate of a parameter of a density operator. It is applied to the estimates of parameters such as amplitude, arrival time, and carrier frequency of a coherent signal as picked up by an ideal receiver in the presence of thermal noise. The estimation of parameters of a noise-like signal is also treated.