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Coherent States and Bayesian Duality

S. Twareque Ali J.-P. Gazeau 1 B. Heller
APC (UMR_7164) - AstroParticule et Cosmologie, Institut für theoretische Physik
Abstract : We demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states, using the concept of a reproducing kernel Hilbert space. Each family of coherent states is shown to contain, in a sort of duality, which resembles an analogous duality in Bayesian statistics, a discrete probability distribution and a discretely parametrized family of continuous distributions. It turns out that nonlinear coherent states, of the type widely studied in quantum optics, are a particularly useful class of coherent states from this point of view, in that they contain many of the standard statistical distributions. We also look at vector coherent states and multidimensional coherent states as carriers of mixtures of probability distributions and joint probability distributions.
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Submitted on : Thursday, January 15, 2009 - 10:52:46 AM
Last modification on : Wednesday, October 21, 2020 - 4:32:12 PM

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S. Twareque Ali, J.-P. Gazeau, B. Heller. Coherent States and Bayesian Duality. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2008, 41, pp.365302. ⟨10.1088/1751-8113/41/36/365302⟩. ⟨in2p3-00353246⟩



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