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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
Experimental demonstration of adaptive quantum state estimation.
Ryo Okamoto,Ryo Okamoto,Minako Iefuji,Minako Iefuji,Satoshi Oyama,Satoshi Oyama,Koichi Yamagata,Hiroshi Imai,Akio Fujiwara,Shigeki Takeuchi,Shigeki Takeuchi +10 more
TL;DR: The first experimental demonstration of AQSE using photons is reported, and the statistical analysis of these results verifies the strong consistency and asymptotic efficiency of AQ SE.
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Optimal estimation of quantum dynamics
TL;DR: In this paper, the optimal strategy for the estimation of an unknown unitary transformation U is an element of SU(d) is presented, in addition to a convenient measurement on a probe system, finding which initial state on which U is to act.
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Discriminating Quantum Optical Beam-splitter Channels with Number Diagonal Signal States: Applications to Quantum Reading and Target Detection
TL;DR: In this article, the authors considered the problem of distinguishing two optical beam-splitter channels with unequal complex-valued reflectivities using general quantum probe states entangled over $M$ signal and ${M}^{\ensuremath{'}}$ idler mode pairs of which the signal modes are bounced off the beam splitter while the idler modes are retained losslessly.
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Quantum knots and mosaics
TL;DR: This paper gives a precise and workable definition of a quantum knot system, the states of which are called quantum knots, and conjecture that this formal system fully captures in an axiomatic way all of the properties of tame knot theory.
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Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
Alex Monras,Fabrizio Illuminati +1 more
TL;DR: In this article, a comprehensive analysis of the performance of different classes of Gaussian states in the estimation of phase-insensitive dissipative channels is presented, in particular, the optimal estimation of the damping constant and reservoir temperature.
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.