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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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Quantum algorithms for Gibbs sampling and hitting-time estimation
TL;DR: This work presents quantum algorithms for solving two problems regarding stochastic processes, one of which estimates the hitting time of a Markov chain and the other quadratically improves the dependence on 1/\epsilon and $1/\Delta of the analog classical algorithm for hitting-time estimation.
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Operational Interpretation of Weight-Based Resource Quantifiers in Convex Quantum Resource Theories
TL;DR: The resource quantifier of weight of resource for convex quantum resource theories of states and measurements with arbitrary resources captures the advantage that a resourceful state offers over all possible free states (measurements) in the operational task of exclusion of subchannels (states).
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Asymptotic estimation theory for a finite-dimensional pure state model
TL;DR: The optimization of measurement for n samples of pure states is studied in this article, where the error of the optimal measurement is asymptotically compared with the one of the maximum likelihood estimators from n data given by the optimal measurements for one sample.
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Quantum metrology with quantum-chaotic sensors
Lukas J. Fiderer,Daniel Braun +1 more
TL;DR: In this article, the hypersensitivity of quantum-chaotic dynamics with respect to parameters of the system has been investigated for spin-precession magnetometry and it has been shown that the sensitivity of state-of-the-art magnetometers can be further enhanced by subjecting the spin precession to non-linear kicks that renders the dynamics chaotic.
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On a measure of distance for quantum strategies
TL;DR: In this article, an operator norm that captures the distinguishability of quantum strategies was proposed. But it is not known whether the trace norm or diamond norm can capture the discriminative properties of quantum channels.
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.