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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 estimation of multiple phases
TL;DR: In this article, the authors studied the problem of simultaneous estimation of several phase shifts induced by commuting operators on a quantum state and derived the optimal positive-operator-valued measure corresponding to the multiple-phase estimation.
Journal ArticleDOI
Subdiffraction incoherent optical imaging via spatial-mode demultiplexing
TL;DR: In this article, a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of spatially incoherent optical sources is proposed, which can estimate its second or higher moments much more precisely than direct imaging can fundamentally do.
Journal ArticleDOI
Optimized communication strategies with binary coherent states over phase noise channels
TL;DR: These novel strategies rely on joint optimization of the input alphabet and the measurement to provide enhanced communication capability over a non-Gaussian channel characterized in terms of the error rate as well as mutual information.
Book ChapterDOI
Quantum Mechanics and Information Retrieval
TL;DR: This chapter describes how the intersection between information retrieval and the quantum mechanical framework has been implemented and presents the most significant contributions to the implementation of this intersection.
Journal ArticleDOI
Resource theory of asymmetric distinguishability for quantum channels
Xin Wang,Xin Wang,Mark M. Wilde +2 more
TL;DR: Two special cases of the general channel box transformation problem, known as distinguishability distillation and dilution, are considered, and it is proved that the exact distinguishability cost is equal to the channel max-relative entropy and the distillable distinguishability isequal to the amortized channel relative entropy.
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
Journal ArticleDOI
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.