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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
Strategies for optimal single-shot discrimination of quantum measurements
Zbigniew Puchała,Zbigniew Puchała,Łukasz Pawela,Łukasz Pawela,Aleksandra Krawiec,Aleksandra Krawiec,Ryszard Kukulski,Ryszard Kukulski +7 more
TL;DR: The main result is a cone program which calculates the distance between the measurements and hence provides an upper bound on the probability of their correct distinction and a full description for the cases of Fourier matrices and mirror isometries.
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Quantum change point
Gael Sentís,Emilio Bagan,John Calsamiglia,Giulio Chiribella,Giulio Chiribella,Ramon Muñoz-Tapia +5 more
TL;DR: This work considers a source that emits quantum particles in a default state, until a point where a mutation occurs that causes the source to switch to another state, and determines the maximum probability of correctly identifying the change point, allowing for collective measurements on the whole sequence of particles emitted by the source.
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Inequalities for quantum Fisher information
TL;DR: In this article, it was shown that Luo's inequality is a particular case of a general inequality which holds for any regular quantum Fisher information, which is a consequence of the Kubo-Ando inequality that states that any matrix mean is bigger than the harmonic mean and smaller than the arithmetic mean.
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Quantum Fisher Information in the Generalized One-axis Twisting Model
TL;DR: In this article, the quantum Fisher information (QFI) of symmetric states for spin-s particles is investigated, and it is shown that quantum spin correlations are essential ingredients of the maximal QFI.
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Weak Decoupling Duality and Quantum Identification
Patrick Hayden,Andreas Winter +1 more
TL;DR: It is established that the optimal amortized rate at which quantum states can be identified through a noisy quantum channel is equal to the entanglement-assisted classical capacity of the channel, despite the fact that the task is quantum, not classical, and entanglements-assistance is not allowed.
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 .
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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.