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Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries

C. Brif·A. Mann
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Abstract

We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical systems possessing Lie-group symmetries. The concept of generalized coherent states and the method of harmonic analysis are used to construct explicitly a family of phase-space functions which are postulated to satisfy the Stratonovich-Weyl correspondence with a generalized traciality condition. The symbol calculus for the phase-space functions is given by means of the generalized twisted product. The phase-space formalism is used to study the problem of the reconstruction of quantum states. In particular, we consider the reconstruction method based on measurements of displaced projectors, which comprises a number of recently proposed quantum-optical schemes and is also related to the standard methods of signal processing. A general group-theoretic description of this method is developed using the technique of harmonic expansions on the phase space.

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C. Brif, A. Mann. 1998-09-17. Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries. https://doi.org/10.1103/physreva.59.971

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