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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
Optimal unambiguous state discrimination of two density matrices: Lower bound and class of exact solutions
TL;DR: In this paper, the authors provide analytical solutions for unambiguous state discrimination of a class of generic mixed states and construct corresponding optimal measurement strategies for two mixed states to reach these bounds.
Journal ArticleDOI
Almost minimum error discrimination of N -ary weak coherent states by Jaynes-Cummings Hamiltonian dynamics
Min Namkung,Younghun Kwon +1 more
TL;DR: This paper proposes the methods where minimum error discrimination of more than two weak coherent states can be nearly performed, and constructs models which can do almost minimum error discriminated states of three and four coherent states.
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Extended number state basis and number-phase intelligent states of light field I. Mapping and operator ordering approach to quantum phase problem
Antonín Lukš,V. Peřinová +1 more
TL;DR: In this paper, the quantum phase problem for single mode optical fields is solved and original definitions of all possible phase operators are given, measures of phase dispersion are reconsidered and the uncertainty relations are modified.
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Tradeoff between energy and error in the discrimination of quantum-optical devices
TL;DR: An analytical derivation of the optimal strategy for beamsplitters and an iterative algorithm converging to the optimum in the general case are provided and a simpler strategy using coherent input states and homodyne detection is compared.
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No-signaling principle can determine optimal quantum state discrimination.
TL;DR: It is shown that, remarkably, the guessing probability can be determined by the no-signaling principle, and it is shown by proving that, in the semidefinite programing for the discrimination, the optimality condition corresponds to the constraint that quantum theory cannot be used for a superluminal communication.
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 .
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.