Coherent States and Bayesian Duality

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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• Coherent states in Quantum Optics: An oriented overview
• Moyal and tomographic probability representations for f-oscillator quantum states
• Lowering Helstrom Bound with non-standard coherent states
• Symmetry in a space of conceptual variables
• Quantization with Action-Angle Coherent States
• SU(1,1)-displaced coherent states, photon counting and squeezing
• Coherent States of Systems with Pure Continuous Energy Spectra
• Generalized 2D Laguerre polynomials and their quaternionic extensions
• Conceptual variables, quantum theory, and statistical inference theory