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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 system identification.
Daniel Burgarth,Kazuya Yuasa +1 more
TL;DR: A basic and general framework is established that allows us to classify how much knowledge about the quantum system is attainable, in principle, from a given experimental setup, and shows that controllable closed quantum systems can be estimated up to unitary conjugation.
Journal ArticleDOI
Explicit formula for the Holevo bound for two-parameter qubit-state estimation problem
TL;DR: In this paper, the Holevo bound for estimating any two-parameter family of qubit mixed-states in terms of quantum versions of Fisher information was derived, based on the symmetric logarithmic derivative (SLD), the right log-linear derivative (RLD) Fisher information and a given weight matrix.
Journal ArticleDOI
Characterization of classical Gaussian processes using quantum probes
TL;DR: In this article, a single qubit is used as a quantum probe to characterize the properties of classical noise arising from the interaction with a stochastic field described by Gaussian processes.
Journal ArticleDOI
Homodyne Estimation of Gaussian Quantum Discord
Rémi Blandino,Marco G. Genoni,Jean Etesse,Marco Barbieri,Matteo G. A. Paris,Philippe Grangier,Rosa Tualle-Brouri,Rosa Tualle-Brouri +7 more
TL;DR: Though homodyne detection is not optimal for Gaussian discord, the noise ratio to the ultimate quantum limit, as dictated by the quantum Cramer-Rao bound, is limited to about 10 dB.
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.