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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 nondemolition measurements: the route from toys to tools
TL;DR: The history of the theory of quantum nondemolition (QND) measurements from the 1920s until today is reviewed in this paper, where the definition and main principles of QND measurements are outlined.
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Submillihertz magnetic spectroscopy performed with a nanoscale quantum sensor
Simon Schmitt,Tuvia Gefen,Felix M. Stürner,Thomas Unden,Gerhard Wolff,Christoph Müller,Jochen Scheuer,Boris Naydenov,Matthew Markham,Sébastien Pezzagna,Jan Meijer,Ilai Schwarz,Martin B. Plenio,Alex Retzker,Liam P. McGuinness,Fedor Jelezko +15 more
TL;DR: A quantum sensing protocol is demonstrated in which the spectral precision goes beyond the sensor coherence time and is limited by the stability of a classical clock.
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Noisy intermediate-scale quantum algorithms
TL;DR: In this article , the authors discuss what is possible in this ''noisy intermediate scale'' quantum (NISQ) era, including simulation of many-body physics and chemistry, combinatorial optimization, and machine learning.
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Unambiguous discrimination between linearly independent quantum states
TL;DR: The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states as mentioned in this paper, and it has been shown that only linearly independent states can be reliably discriminated.
Book
Quantum Measurement Theory and its Applications
TL;DR: In this article, the authors present a survey of quantum mesoscopic systems and their applications in information theory, statistical mechanics, open systems, and measurement, as well as quantum feedback control.
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.