Phase-space formulation of quantum mechanics and quantum-state reconstruction for physical systems with Lie-group symmetries
Year: 1999
Type: article
Abstract: We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A 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 tracing 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.
Source: Physical Review A
Institution: Technion – Israel Institute of Technology
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2078412318