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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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The modern tools of quantum mechanics - A tutorial on quantum states, measurements, and operations
TL;DR: In this paper, the authors review the modern tools of quantum mechanics, which are suitable to describe states, measurements, and operations of realistic, not isolated, systems, and illustrate how the notion of density operator naturally emerges, together with the concept of purification of a mixed state.
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Classical interventions in quantum systems. I. The measuring process
TL;DR: The measuring process is an external intervention in the dynamics of a quantum system as discussed by the authors, which involves a unitary interaction of that system with a measuring apparatus, a further interaction of both with an unknown environment causing decoherence, and then the deletion of a subsystem.
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Local asymptotic normality in quantum statistics
Madalin Guta,Anna Jenčová +1 more
TL;DR: In this paper, the theory of local asymptotic normality for quantum statistical experiments is developed in the spirit of the classical result from mathematical statistics due to Le Cam, and the convergence holds for all "local parameters" u ∈ Theta ∈ R^{m} such that theta=theta 0+ u ∆ ∆+ ∆ + ∆/ ∆ n/sqrt{n} parametrizes a neighborhood of a fixed point theta 0 in Theta subset R ∆.
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Optimal estimation of entanglement
TL;DR: In this article, the optimal estimation of entanglement in the framework of local quantum estimation theory and derive the optimal observable in terms of the symmetric logarithmic derivative.
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Quantum multiparameter metrology with generalized entangled coherent state
TL;DR: In this article, a generalized form of entangled coherent states (ECS) was proposed and applied in a multi-arm optical interferometer to estimate multiple phase shifts. And the quantum Cramer-Rao bounds for both the linear and nonlinear parametrization protocols were obtained.
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 .
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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.