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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
Geometric measures of quantum correlations : characterization, quantification, and comparison by distances and operations
TL;DR: In this article, the authors compare three geometric measures of bipartite quantum correlations: geometric discord, measurement-induced geometric discord and the discord of response, each one defined according to three contractive distances on the set of quantum states, namely the trace, Bures, and Hellinger distances.
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Quantum variance: A measure of quantum coherence and quantum correlations for many-body systems
TL;DR: In this article, a quantitative definition of the variance of quantum coherent fluctuations (the quantum variance) of any observable on generic quantum states is provided, which generalizes the concept of thermal de Broglie wavelength (for the position of a free quantum particle) to quantifying the degree of coherent delocalization in that space.
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Phase-sensitivity bounds for two-mode interferometers
TL;DR: In this paper, the authors provided general bounds of phase estimation sensitivity in linear two-mode interferometers and showed that particle entanglement is necessary but not sufficient to overcome the shot noise limit.
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Sequential attacks against differential-phase-shift quantum key distribution with weak coherent states
TL;DR: This work analyzes two sequential attacks based on unambiguous state discrimination and minimum error discrimination of the signal states emitted by the source of pulsed coherent light to determine the ultimate upper bounds on the maximal distance achievable by quantum key distribution schemes.
Journal Article
Optimal measurements for the dihedral hidden subgroup problem
TL;DR: In this paper, the authors consider the problem of identifying hidden subgroup states in a dihedral group and show that the optimal measurement for solving this problem is the so-called pretty good measurement.
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.