相关论文: Dispelling Rayleigh's Curse

The quantity of interest in the classical Cram\'er-Rao theory of unbiased estimation (e.g., the Cram\'er-Rao lower bound, its exact attainment for exponential families, and asymptotic efficiency of maximum likelihood estimation) is the…

We introduce the notion of the essential tangent bundle of a parametrized measure model and the notion of reduced Fisher metric on a (possibly singular) 2-integrable measure model. Using these notions and a new characterization of…

A general expression for the optical theorem for probe sources given in terms of propagation invariant beams is derived. This expression is obtained using the far field approximation for Rayleigh regime. In order to illustrate this results…

It is known that weak measurement can significantly amplify the mean of measurement results, sometimes out of the range limited in usual quantum measurement. This fact, as actively demonstrated recently in both theory and experiment,…

Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…

We propose a new scheme to achieve sub-Rayleigh resolution of interference pattern with independent laser beams. We perform an experimental observation of a double-slit interference with two orthogonally polarized laser beams. The…

We consider the problem of estimating a structured multivariate density, subject to Markov conditions implied by an undirected graph. In the worst case, without Markovian assumptions, this problem suffers from the curse of dimensionality.…

The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the…

The optimal quantum measurements for estimating individual parameters might be incompatible with each other so that they cannot be jointly performed. The tradeoff between the estimation precision for different parameters can be…

Detection of radiation signals is at the heart of precision metrology and sensing. In this article we show how the fluctuations in photon counting signals can be exploited to optimally extract information about the physical parameters that…

Inverse source problems are central to many applications in acoustics, geophysics, non-destructive testing, and more. Traditional imaging methods suffer from the resolution limit, preventing distinction of sources separated by less than the…

By encoding the high-dimensional light-field imaging information into a detectable two-dimensional speckle plane, ghost imaging camera via sparsity constraints (GISC camera) can directly catch the high-dimensional light-field imaging…

The classical Cram\'er-Rao inequality gives a lower bound for the variance of a unbiased estimator of an unknown parameter, in some statistical model of a random process. In this note we rewrite the statment and proof of the bound using…

A general class of Bayesian lower bounds when the underlying loss function is a Bregman divergence is demonstrated. This class can be considered as an extension of the Weinstein--Weiss family of bounds for the mean squared error and relies…

Imaging point sources with low angular separation near or below the Rayleigh criterion is important in astronomy, e.g., in the search for habitable exoplanets near stars. However, the measurement time required to resolve stars in the…

In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…

The problem of estimating multiple loss parameters of an optical system using the most general ancilla-assisted parallel strategy is solved under energy constraints. An upper bound on the quantum Fisher information matrix is derived…

We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…

We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all…

This paper is devoted to the analysis of the angular resolution limit (ARL), an important performance measure in the directions-of-arrival estimation theory. The main fruit of our endeavor takes the form of an explicit, analytical…