2022/02/21 by Kwan Kit Lee, Christos N. Gagatsos, Lee, Kwan Kit +5
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Advanced Fluorescence Microscopy Techniques #Data Analysis #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Quantum Physics (quant-ph) #Sparse and Compressive Sensing Techniques #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2202.09980
openalex publication_date 2022/02/21 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In Bayesian estimation theory, the estimator θ = E[θ|l] attains the minimum mean squared error (MMSE) for estimating a scalar parameter of interest θ from the observation of l through a noisy channel Pl|θ, given a prior Pθ on θ. In quantum sensing tasks, the user gets ρθ, the quantum state that encodes θ. They choose a measurement, a positive-operator valued measure (POVM) Πl, which induces the channel Pl|θ = \rm Tr(ρθΠl) to the measurement outcome l, on which the aforesaid classical MMSE estimator is employed. Personick found the optimum POVM Πl that minimizes the MMSE over all possible measurements, and that MMSE. This result from 1971 is less-widely known than the quantum Fisher information (QFI), which lower bounds the variance of an unbiased estimator over all measurements, when Pθ is unavailable. For multi-parameter estimation, i.e., when θ is a vector, in Fisher quantum estimation theory, the inverse of the QFI matrix provides an operator lower bound to the covariance of an unbiased estimator. However, there has been little work on quantifying quantum limits and measurement designs, for multi-parameter quantum estimation in the \em Bayesian setting. In this paper, we build upon Personick's result to construct a Bayesian adaptive measurement scheme for multi-parameter estimation when N copies of ρθ are available. We illustrate an application to localizing a cluster of point emitters in a highly sub-Rayleigh angular field-of-view, an important problem in fluorescence microscopy and astronomy. Our algorithm translates to a multi-spatial-mode transformation prior to a photon-detection array, with electro-optic feedback to adapt the mode sorter. We show that this receiver performs far superior to quantum-noise-limited focal-plane direct imaging.