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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
Maximum Fisher information in mixed state quantum systems
TL;DR: In this article, the authors derived the expression of the maximum Fisher information achievable and its relation with that attainable in pure states and showed that this condition holds even in the more general setting of two-dimensional mixed state systems.
Journal ArticleDOI
Base norms and discrimination of generalized quantum channels
TL;DR: This work obtains a necessary and sufficient condition under which an optimal 1-tester for discrimination of quantum channels exists, such that the input state is maximally entangled.
Journal ArticleDOI
Multiparameter estimation with single photons—linearly-optically generated quantum entanglement beats the shotnoise limit
Chenglong You,Sushovit Adhikari,Yuxi Chi,Margarite L. LaBorde,Corey T. Matyas,Chenyu Zhang,Zu-En Su,Tim Byrnes,Tim Byrnes,Chao-Yang Lu,Jonathan P. Dowling,Jonathan P. Dowling,Jonathan P. Olson +12 more
TL;DR: In this article, the quantum Cramer-Rao bound for multi-parameter estimation of optical networks with single photon Fock states, passive optical elements, and single photon detection was analyzed.
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Resolution of point sources of light as analyzed by quantum detection theory
TL;DR: The resolvability of point sources of incoherent thermal light is analyzed by quantum detection theory in terms of two hypothesis-testing problems, where either one, but not both, of two point sources is radiating, and the observer must decide which it is.
Posted Content
Precision bounds in noisy quantum metrology
TL;DR: In this article, it was shown that an infinitesimal amount of noise is enough to restrict the precision to scale classically in the asymptotic $N$ limit, and thus constrain the maximal improvement to a constant factor.
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 .
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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.