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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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Maximum-likelihood estimation of quantum measurement
TL;DR: In this article, the maximum likelihood estimation is applied to the determination of unknown quantum measurements, and the positive operator-valued measure governing the measurement statistics is inferred from the collected data via the maximum-likelihood principle.
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Optimal quantum estimation of the Unruh-Hawking effect.
TL;DR: It is proved that a field in a Fock inertial state, probed via photon counting by a noninertial detector, realizes the optimal strategy attaining the ultimate sensitivity allowed by quantum mechanics for the observation of the Unruh-Hawking effect.
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Beating Rayleigh's Curse by Imaging Using Phase Information
TL;DR: A simple scheme is experimentally demonstrated that captures most of the information in the full electromagnetic field in the image plane and has a greatly improved ability to estimate the distance between a pair of closely separated sources, achieving near-quantum-limited performance and immunity to Rayleigh's curse.
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Computable bounds for the discrimination of Gaussian states
Stefano Pirandola,Seth Lloyd +1 more
TL;DR: By combining the Minkowski inequality and the quantum Chernoff bound, easy-to-compute upper bounds for the error probability affecting the optimal discrimination of Gaussian states are derived.
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Geometric derivation of the quantum speed limit
Philip J. Jones,Pieter Kok +1 more
TL;DR: In this article, alternative geometric derivations for the Mandelstam-Tamm and Margolus-Levitin inequalities are obtained from the statistical distance between quantum states.
References
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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 .
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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.