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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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Quantum discord and its allies: a review of recent progress.
TL;DR: In this paper, a review of concepts and methods associated with quantum discord and related topics is presented, as well as their possible connections with other aspects of quantum information and beyond, including quantum communication, quantum computation, many-body physics, and open quantum dynamics.
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Quantum channels and their entropic characteristics
TL;DR: A survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite-dimensional quantum systems, and the remarkable role of specific quantum correlations-entanglement-as a novel communication resource is stressed.
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Optimum measurements for discrimination among symmetric quantum states and parameter estimation
TL;DR: In this paper, an optimum quantum measurement that minimizes the average probability of error for symmetric quantum states was derived by using the quantum Bayes strategy, and it was shown that the mutual information obtained in the optimum measurement becomes extremum.
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Multi-parameter quantum metrology
TL;DR: In this paper, the authors review the background of quantum-limited local estimation theory of multiple parameters that underlies these advances and discuss some of the main results in the field and its recent progress.
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A new approach to the Cramér-Rao-type bound of the pure-state model
TL;DR: In this article, the quantum Cramer-Rao-type bound for many cases was calculated using a newly proposed powerful technique, and the use of collective measurement in statistical estimation was discussed.
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.