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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 Zeno effect by general measurements
TL;DR: In this paper, the authors considered a continuous measurement of the decay of an excited atom by a photodetector that detects a photon emitted from the atom upon decay, and showed that the form factor is renormalized as a backaction of the measurement, through which the decay dynamics is modified.
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The chernoff lower bound for symmetric quantum hypothesis testing
Michael Nussbaum,Arleta Szkola +1 more
TL;DR: A lower bound on the asymptotic rate exponents of Bayesian error probabilities is proved, which represents a quantum extension of the Chernoff bound, which gives the best asymPTotically achievable error exponent in classical discrimination between two probability measures on a finite set.
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Error exponent in asymmetric quantum hypothesis testing and its application to classical-quantum channel coding
TL;DR: In this paper, an upper bound on simple quantum hypothesis testing in the asymmetric setting is shown using a useful inequality by Audenaert et al. using this upper bound, they obtain the Hoeffding bound which is identical with the classical counterpart if the hypotheses, composed of two density operators, are mutually commutative.
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Optimum unambiguous discrimination between linearly independent symmetric states
TL;DR: In this article, the maximum probability with which a set of equally likely, symmetric, linearly independent states can be discriminated was obtained for symmetric coherent states of a harmonic oscillator or field mode.
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Soundness and completeness of quantum root-mean-square errors
TL;DR: In this paper, Ozawa et al. proposed an improved root-mean-square (RMS) metric for quantum measurement uncertainty relation, which is state-dependent, operationally definable and perfectly characterizes accurate measurements.
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.