Joint optimal measurement for locating two incoherent optical point sources near the Rayleigh distance. (1st April 2023)

• Record Type: Journal Article
• Authors: Shi, Yingying; Lu, Xiao-Ming
• Is Part Of: Communications in theoretical physics. Volume 75:Number 4(2023)
• Publication Date: 2023-04-01
• Subjects: quantum metrology -- quantum parameter estimation -- quantum measurement -- quantum imaging; Physics -- Periodicals; 530.105
• DOI: 10.1088/1572-9494/acc4ae
• Languages: English
• ISSNs: 0253-6102

Abstract

Abstract: Simultaneously optimizing the estimation of the centroid and separation of two incoherent optical point sources is constrained by a tradeoff relation determined by an incompatibility coefficient. 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. 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.