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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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Book ChapterDOI
Quantum Limits in Optical Interferometry
TL;DR: In this paper, the authors summarize the developments of quantum metrology with particular focus on optical interferometry and derive fundamental bounds on achievable quantum-enhanced precision in optical inter-ferometry taking into account the most relevant decoherence processes including phase diffusion, losses, and imperfect interferometric visibility.
Journal ArticleDOI
Concepts of quantum non-Markovianity: a hierarchy
TL;DR: In this article, a host of Markov-related concepts in the quantum regime are studied, such as quantum white noise, factorization approximation, divisibility, and GKS-Lindblad master equation.
Journal ArticleDOI
Violation of the Leggett–Garg inequality with weak measurements of photons
M. E. Goggin,Marcelo P. Almeida,Marco Barbieri,B. P. Lanyon,Jeremy L. O'Brien,Andrew White,Geoff J. Pryde +6 more
TL;DR: By weakly measuring the polarization of a photon between two strong polarization measurements, this work experimentally investigates the correlation between the appearance of anomalous values in quantum weak measurements and the violation of realism and nonintrusiveness of measurements.
Posted Content
Distinguishability and Accessible Information in Quantum Theory
TL;DR: This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states, and gives a way of expressing the problem so that it appears as algebraic as that of the problem of finding quantum distinguishability measures.
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.