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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 channels and memory effects
TL;DR: The study of memory effects in quantum channels is a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics.
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Quantum Fisher information matrix and multiparameter estimation
TL;DR: In this paper, the authors summarize the properties and existing calculation techniques of quantum Fisher Information Matrix (QFIM) for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology.
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Quantum-state disturbance versus information gain: Uncertainty relations for quantum information
Christopher A. Fuchs,Asher Peres +1 more
TL;DR: The trade-off between the information gain and that disturbance in the act of observation is investigated, and the optimal detection method is explicitly found in the case of two equiprobable nonorthogonal pure states.
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Area laws in a many-body localized state and its implications for topological order
Bela Bauer,Chetan Nayak +1 more
TL;DR: In this paper, it was shown that a single energy eigenstate of a Hamiltonian can be adiabatically connected to a state of a non-interacting Anderson insulator.
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Using entanglement against noise in quantum metrology.
TL;DR: It is proved that entangled strategies can have higher precision than unentangled ones and that the addition of passive external ancillas can also increase the precision.
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.