Open AccessBook
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
Optimal quantum states for frequency estimation
TL;DR: In this paper, the authors investigate different quantum parameter estimation scenarios in the presence of noise, and identify optimal probe states for up to 70 qubits, and determine their key properties.
Book Chapter
On Asymptotic Quantum Statistical Inference
Richard D. Gill,Madalin Guta +1 more
TL;DR: In this paper, asymptotically optimal statistical inference concerning the unknown state of $N$ identical quantum systems, using two complementary approaches: a "poor man's approach" based on the van Trees inequality, and a rather more sophisticated approach using the recently developed quantum form of LeCam's theory of Local Asymptotic Normality.
Journal ArticleDOI
Hong-Ou-Mandel interferometry on a biphoton beat note
Yuanyuan Chen,Yuanyuan Chen,Yuanyuan Chen,Matthias Fink,Matthias Fink,Fabian Steinlechner,Fabian Steinlechner,Juan P. Torres,Juan P. Torres,Rupert Ursin,Rupert Ursin +10 more
TL;DR: In this article, the authors show that the use of two well-separated frequencies embedded in a quantum entangled state (discrete color entanglement) suffices to achieve great precision.
Journal ArticleDOI
Rényi formulation of the entropic uncertainty principle for POVMs
TL;DR: Uncertainty relations for a pair of arbitrary measurements are posed in the form of inequalities using the Renyi entropies using state-dependent and state-independent bounds.
Journal ArticleDOI
Optimal measurements for general quantum systems
TL;DR: In this article, a general formulation of the theory of optimal quantum measurements, based on Gudder's convex structure approaches to axiomatic quantum mechanics, is given, and simple and general conditions for existence of Bayes optimal measurements are obtained by a method without operator valued measure techniques.
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
Journal ArticleDOI
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.