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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
Experimental adaptive Bayesian estimation of multiple phases with limited data
Mauro Valeri,Emanuele Polino,Davide Poderini,Ilaria Gianani,Ilaria Gianani,Giacomo Corrielli,Andrea Crespi,Roberto Osellame,Nicolò Spagnolo,Fabio Sciarrino +9 more
TL;DR: This work investigates and implements experimentally an adaptive Bayesian multiparameter estimation technique tailored to reach optimal performances with very limited data, and shows that adaptive strategies can become a viable approach for realistic sensors working with a limited amount of resources.
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Mixing-induced quantum non-Markovianity and information flow
TL;DR: In this paper, the authors show that mixing-induced non-Markovianity can be interpreted in terms of the distinguishability of quantum states, system-environment correlations and the information flow between system and environment.
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Quantum metrology assisted by abstention.
TL;DR: This work shows that abstention, i.e., the possibility of getting an inconclusive answer at readout, can drastically improve the measurement precision and even lead to a change in its asymptotic behavior, from the shot-noise to the Heisenberg scaling.
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Multi-state discrimination below the quantum noise limit at the single-photon level
TL;DR: The discrimination of multiple coherent states of light with sensitivities surpassing the quantum noise limit at the single-photon level under realistic conditions of loss and noise based on strategies implementing globally-optimized adaptive measurements with single photon counting and displacement operations is studied.
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Maximal quantum Fisher information for general su(2) parametrization processes
TL;DR: In this paper, the maximal quantum Fisher information of the Hermitian operator of a general unitary parametrization process is derived for a driving field with a time-dependent Hamiltonian.
References
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Journal ArticleDOI
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.