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Quantum detection and estimation theory
TLDR
In this article, the optimum procedure for choosing between two hypotheses, and an approximate procedure valid at small signal-to-noise ratios and called threshold detection, are presented, and a quantum counterpart of the Cramer-Rao inequality of conventional statistics sets a lower bound to the mean-square errors of such estimates.Abstract:
A review. Quantum detection theory is a reformulation, in quantum-mechanical terms, of statistical decision theory as applied to the detection of signals in random noise. Density operators take the place of the probability density functions of conventional statistics. The optimum procedure for choosing between two hypotheses, and an approximate procedure valid at small signal-to-noise ratios and called threshold detection, are presented. Quantum estimation theory seeks best estimators of parameters of a density operator. A quantum counterpart of the Cramer-Rao inequality of conventional statistics sets a lower bound to the mean-square errors of such estimates. Applications at present are primarily to the detection and estimation of signals of optical frequencies in the presence of thermal radiation.read more
Citations
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Journal ArticleDOI
Quantum phase estimation with lossy interferometers
Rafał Demkowicz-Dobrzański,U. Dorner,Brian J. Smith,Brian J. Smith,Jeff S. Lundeen,Wojciech Wasilewski,Konrad Banaszek,Ian A. Walmsley +7 more
TL;DR: In this paper, a detailed discussion of optimal quantum states for optical two-mode interferometry in the presence of photon losses is given. And the corresponding optimal precision, i.e., the lowest possible uncertainty, is shown to beat the standard quantum limit.
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Multiparameter Estimation in Networked Quantum Sensors
TL;DR: It is shown that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network, which applies to any situation in which spatially localized sensors are unitarily encoded with independent parameters.
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Quantum feedback: Theory, experiments, and applications
TL;DR: In this article, an introductory overview of the various ways in which feedback may be implemented in quantum systems, the theoretical methods that are currently used to treat it, the experiments in which it has been demonstrated to date, and its applications.
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A Resource Framework for Quantum Shannon Theory
TL;DR: This paper advocates a unified approach to an important class of problems in quantum Shannon theory, consisting of those that are bipartite, unidirectional, and memoryless.
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Quantum criticality as a resource for quantum estimation
TL;DR: In this paper, the authors consider quantum critical systems as a resource in quantum estimation and derive the ultimate quantum limits to the precision of any estimator of the coupling parameters of a quantum phase transition.
References
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Journal ArticleDOI
Coherent and incoherent states of the radiation field
TL;DR: In this article, the photon statistics of arbitrary fields in fully quantum-mechanical terms are discussed, and a general method of representing the density operator for the field is discussed as well as a simple formulation of a superposition law for photon fields.
Book
Detection, Estimation, And Modulation Theory
TL;DR: Detection, estimation, and modulation theory, Detection, estimation and modulation theorists, اطلاعات رسانی کشاورزی .
Journal ArticleDOI
Description of States in Quantum Mechanics by Density Matrix and Operator Techniques
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On the problems of the most efficient tests of statistical hypotheses.
J. Neyman,E. S. Pearson +1 more
TL;DR: The problem of testing statistical hypotheses is an old one as discussed by the authors, and its origin is usually connected with the name of Thomas Bayes, who gave the well-known theorem on the probabilities a posteriori of the possible causes of a given event.