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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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Precision thermometry and the quantum speed limit
TL;DR: In this article, the authors show that the gap sets a single temperature that can be optimally estimated, and establish a simple linear relationship between the gap and this temperature, and demonstrate that the precision exhibits a quadratic relationship.
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Optimal Estimation of Qubit States with Continuous Time Measurements
TL;DR: In this paper, an adaptive two-step strategy for the estimation of mixed qubit states is proposed, which is asymptotically Bayesian optimal for a large class of prior distributions.
Posted Content
Non-classical correlations in quantum mechanics and beyond /
TL;DR: In this paper, the authors consider the problem of data hiding in the context of general probabilistic theories (GPTs) and present a tracta to answer the question: "Is it possible to pertany l'entrellacament exclusivament als sistemes quantics or es comu a totes les teories no classiques?"
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Nonclassical time correlation functions in continuous quantum measurement
TL;DR: In this article, the authors analyze the stochastic properties of this uncertainty component in the resulting observation trajectory, and demonstrate a violation of classical macrorealism using the fourth-order time correlation functions with respect to the quasi-probability in the two-level system.
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Quantum receivers with squeezing and photon-number-resolving detectors for M -ary coherent state discrimination
TL;DR: In this article, two types of quantum receivers with optical squeezing and photon-number-resolving detectors (PNRDs) were proposed for the near-optimal discrimination of quaternary phase-shift-keyed coherent state signals.
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.