6 research outputs found
Direct sampling of exponential phase moments of smoothed Wigner functions
We investigate exponential phase moments of the s-parametrized
quasidistributions (smoothed Wigner functions). We show that the knowledge of
these moments as functions of s provides, together with photon-number
statistics, a complete description of the quantum state. We demonstrate that
the exponential phase moments can be directly sampled from the data recorded in
balanced homodyne detection and we present simple expressions for the sampling
kernels. The phase moments are Fourier coefficients of phase distributions
obtained from the quasidistributions via integration over the radial variable
in polar coordinates. We performed Monte Carlo simulations of the homodyne
detection and we demonstrate the feasibility of direct sampling of the moments
and subsequent reconstruction of the phase distribution.Comment: RevTeX, 8 pages, 6 figures, accepted Phys. Rev.
Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries
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.Comment: REVTeX, 18 pages, no figure