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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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Better Bell-inequality violation by collective measurements
TL;DR: In this paper, the authors investigated the possibility of increasing the violation of a Bell inequality by making collective measurements, and they showed that the nonlocality of pure entangled states, quantified by their maximal violation of the Bell-Clauser-Horne inequality, can always be enhanced by collective measurements.
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Conservative classical and quantum resolution limits for incoherent imaging
TL;DR: In this article, classical and quantum limits to the statistical resolution of two incoherent optical point sources from the perspective of minimax parameter estimation were proposed based on the worst-case error criterion and a Bayesian version of the Cramer-Rao bound.
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Quantum reading under a local energy constraint
TL;DR: In this article, the critical number of signal modes after which a non-classical source of light is able to beat any classical source irradiating the same number of signals is investigated.
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Magnetometry via a double-pass continuous quantum measurement of atomic spin
TL;DR: In this article, it was shown that it is possible to reduce the uncertainty of an atomic magnetometer by double passing a far-detuned laser field through the atomic sample as it undergoes Larmor precession.
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PT-symmetric quantum state discrimination
TL;DR: The objective of this paper is to explain and elucidate the formalism of quantum mechanics by applying it to a well-known problem in conventional Hermitian quantum mechanics, namely the problem of state discrimination, and it is shown that it is always possible to choose the inner product that is appropriate for the Hilbert space of physical states.
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.