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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
Local Distinguishability of Any Three Quantum States
TL;DR: In this paper, it was shown that any three linearly independent pure quantum states can always be locally distinguished with nonzero probability regardless of their dimension, entanglement or multipartite structure.
Journal ArticleDOI
Gaussian Interferometric Power
TL;DR: In this article, the interferometric power of a bipartite quantum state quantifies the precision, measured by quantum Fisher information, that such a state enables for the estimation of a parameter embedded in a unitary dynamics applied to one subsystem only, in the worstcase scenario where a full knowledge of the generator of the dynamics is not available a priori.
Journal ArticleDOI
Past of a quantum particle revisited
Berthold-Georg Englert,Berthold-Georg Englert,Kelvin Horia,Jibo Dai,Yink Loong Len,Hui Khoon Ng,Hui Khoon Ng,Hui Khoon Ng +7 more
TL;DR: Danan et al. as mentioned in this paper analyzed Vaidman's three-path interferometer with weak path marking and found that common sense yields correct statements about the particle's path through the interferometers.
Posted Content
Sending quantum entanglement through noisy channels
TL;DR: This paper addresses some general questions of quantum information theory arising from the transmission of quantum entanglement through (possibly noisy) quantum channels and some insight can be gained into the security of quantum cryptographic protocols and the nature of quantum error-correcting codes.
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Implementation of projective measurements with linear optics and continuous photon counting
TL;DR: In this paper, the authors investigate the possibility of implementing a given projection measurement using linear optics and arbitrarily fast feedforward based on the continuous detection of photons, and they systematically derive the so-called Dolinar scheme that achieves the minimum-error discrimination of binary coherent states.
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
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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.