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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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Optimal Measurement and Control in Quantum Dynamical Systems
TL;DR: In this article, a multi-stage version of quantum measurement and statistical decisions applied to the optimal control problem for quantum dynamical discrete-time objects is developed, where quantum analogies of Stratonovich non-stationary ltering and Bellman quantum dynamic programming for the time being discrete are obtained.
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State Discrimination With Post-Measurement Information
TL;DR: In this article, the authors introduce a new state discrimination problem in which we are given additional information about the state after the measurement, or more generally after a quantum memory bound applies.
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Neural-Network Heuristics for Adaptive Bayesian Quantum Estimation
TL;DR: It is shown that neural networks can be trained to become fast and strong experiment-design heuristics using a combination of an evolutionary strategy and reinforcement learning and are shown to outperform establishedHeuristics for the technologically important example of frequency estimation of a qubit that suffers from dephasing.
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Quantum state estimation with nuisance parameters
TL;DR: In this paper, the authors provide a systematic review of quantum estimation in the presence of nuisance parameters, and provide those who work in quantum tomography and quantum metrology with tools to tackle relevant problems.
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Discriminating strength: a bona fide measure of non-classical correlations
TL;DR: Girolami et al. as mentioned in this paper introduced a measure of non-classical correlations and characterized the maximum value of their nonclassicality measure over a set of separable configurations, which admit a statistical unravelling where each element of the associated ensemble is distinguishable via local measures.
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.