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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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Master equation for retrodiction of quantum communication signals.
TL;DR: The master equation that governs the evolution of the measured state backwards in time in an open system is derived, which allows us to determine probabilities for a given set of preparation events from the results of subsequent measurements, which has particular relevance to quantum communication.
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Covariant quantum measurements that maximize the likelihood
TL;DR: In this article, the authors derived the class of covariant measurements that are optimal according to the maximum likelihood criterion for pure input states, under the physically meaningful hypotheses of unimodularity of the covariance group and measurability of the stability subgroup.
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Extended convexity of quantum Fisher information in quantum metrology
S. Alipour,Ali T. Rezakhani +1 more
TL;DR: In this article, an extended convexity for quantum Fisher information of a mixed state with a given convex decomposition is presented, which introduces a bound which has two parts: (i) the classical part associated with the probability distribution of the states contributing to the decomposition, and (ii) the quantum part given by the average quantum Fisher Information of states in this decomposition.
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Bayesian multiparameter quantum metrology with limited data
TL;DR: A Bayesian multi-parameter quantum bound is derived, the optimal measurement when the authors' bound can be saturated for a single shot is constructed, and experiments involving a repeated sequence of these measurements are considered.
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Motional Fock states for quantum-enhanced amplitude and phase measurements with trapped ions.
Fabian Wolf,Chunyan Shi,Jan C. Heip,Manuel Gessner,Luca Pezzè,Augusto Smerzi,Marius Schulte,Klemens Hammerer,Piet O. Schmidt,Piet O. Schmidt +9 more
TL;DR: A phase-insensitive Fock-state-based protocol for displacement and frequency metrology that is insensitive to the quantum noise of the vacuum, and is demonstrated using trapped ions.
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.