Optimized Measurement For Two Incoherent Point Sources

In the imaging system of two point light sources,resolution is an important basis for evaluating the imaging performance of the imaging system.The ideal resolution of two incoherent point light source imaging systems,most famous and influential method is the Rayleigh criterion.However,resolution is affected by diffraction,and the ”Rayleigh curse” phenomenon occurs when the separation between two incoherent point sources is less than the diffraction limit.In order to break through the ”Rayleigh curse” phenomenon,one began to use quantum theory to surpass previous classical methods.For the efficiency of the resolution of two incoherent point light sources,We can use Fisher information to evaluate.Quantum Fisher information is the limit of the resolution that we can obtain,and classical Fisher information can better improve the resolution in quantum measurement theory.In the measurement of two incoherent point light sources,we use information regret to describe the constraints of centroid and separation,so that we can quantitatively characterize the performance gap of quantum measurements compared to the optical measurement in estimating unknown parameters.The simultaneous optimization of the centroid estimation and the separation estimation of two incoherent optical point sources is restricted by a tradeoff relation through an incompatibility coefficient.The study shows that at the Rayleigh distance the incompatibility coefficient vanishes and thus the tradeoff relation no longer restricts the simultaneous optimization of measurement for a joint estimation.In this paper,we will obtain considerable optimization results by numerical optimization measurements using the method of random measurement.In addition,we construct such a joint optimal measurement by an elaborated analysis on the operator algebra of the symmetric logarithmic derivative.Our work not only confirms the existence of a joint optimal measurement for this specific imaging model,but also gives a promising method to characterize the condition on measurement compatibility for general multiparameter estimation problems.