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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
Quantum Enhanced Estimation of a Multidimensional Field.
Tillmann Baumgratz,Animesh Datta +1 more
TL;DR: In this article, a framework for the quantum enhanced estimation of multiple parameters corresponding to noncommuting unitary generators is presented, and a probe state that surpasses the precision of estimating the three components individually, and measurements that come close to attaining the quantum limit.
Journal ArticleDOI
Practical private database queries based on a quantum-key-distribution protocol
Markus Jakobi,Markus Jakobi,Christoph Simon,Christoph Simon,Nicolas Gisin,Jean-Daniel Bancal,Cyril Branciard,Nino Walenta,Hugo Zbinden +8 more
TL;DR: This work proposes to implement private queries based on a quantum-key-distribution protocol, with changes only in the classical postprocessing of the key, which makes the scheme both easy to implement and loss tolerant.
Book ChapterDOI
Machine learning in a quantum world
TL;DR: An investigation of the encounter of ML with QIP is initiated by defining and studying novel learning tasks that correspond to Machine Learning in a world in which the information is fundamentally quantum mechanical.
Journal ArticleDOI
Achieving the Heisenberg limit in quantum metrology using quantum error correction
TL;DR: In this article, a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed.
Journal ArticleDOI
Quantum information and precision measurement
TL;DR: Some applications of quantum information theory to the analysis of quantum limits on measurement sensitivity are described, including superdense coding, fast database search, and the quantum Fourier transform.
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.