Quantum Parameter Estimation Of Incoherent Signals

Measurement is an important approach for human beings to explore the nature and is also an important content in physics and engineering science.In the scientific researches,one often needs measurements with extremely high precision,such as those for quantum frequency standard,atomic clock,and the detection of gravitational waves.The measurement precision is determined by the randomness within observations.In quantum mechanics,the outcomes of quantum measurement are intrinsically random.This random nature of quantum measurement imposes a fundamental limit on the measurement precision and the measurements attaining the fundamental quantum limit are optimal.Quantum parameter estimation is a theory about the limits on estimation errors with quantum systems.The most useful tools in quantum parameter estimation is the quantum Cramer-Rao bound with quantum Fisher information.For concrete estimation problems,one can obtain the fundamental limit on estimation errors by calculating the quantum Fisher information.Recently,applying quantum parameter estimation on the problem of distinguishing two incoherent optical point sources,it is found that direct imaging is far away from being optimal.This reveals that even the optical field from each source have overlap,it can still be distinguished very well with the optimal quantum measurement.In this thesis,we generalize this problem to the estimation of signals with incoherent sources and propose the concept of curse matrix to reflect the impact from the overlap between state vectors on the estimation precision.We use the method of nonorthonormal basis to derive the expression of curse matrix and prove the necessary and sufficient condition on the vanishing of the curse matrix.We also give an analytic expression of the curse matrix for the cases of two incoherent sources.