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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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Optimal measurements for quantum multiparameter estimation with general states
TL;DR: In this article, the authors generalize the approach by Braunstein and Caves to quantum multiparameter estimation with general states, and derive a matrix bound of the classical Fisher information matrix due to each measurement operator.
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Witnessing entanglement without entanglement witness operators
TL;DR: The proposed method is remarkably simple: multipartite entanglement is witness without relying on the tomographic reconstruction of the quantum state, or the realization of witness operators, and is robust against noise and decoherence occurring after the implementation of the parametric transformation.
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Quantum perfect correlations
TL;DR: The notion of perfect correlations between observables and POVMs was introduced in the standard formulation of quantum mechanics, and characterized by several well-established statistical conditions as discussed by the authors, and the transitivity of perfect correlation is proved to generally hold, and applied to a simple articulation for the failure of Hardy's nonlocality proof for maximally entangled states.
Posted Content
Quantum Knots and Mosaics
TL;DR: In this paper, the authors give a precise and workable definition of a quantum knot system, the states of which are called quantum knots, which can be viewed as a blueprint for the construction of an actual physical quantum system.
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Minimum Decision Cost for Quantum Ensembles
TL;DR: The results obtained prove that, for arbitrarily given values of the prior probabilities and an arbitrary number of constituent particles, the cost of a combined measurement is the same as that for sequential measurements of the individual particles.
References
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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.