A General Theory of Phase-Space Quasiprobability Distributions

Abstract

We present a general theory of quasiprobability distributions on phase spaces of quantum systems whose dynamical symmetry groups are (finite-dimensional) Lie groups. The family of distributions on a phase space is postulated to satisfy the Stratonovich-Weyl correspondence with a generalized traciality condition. The corresponding family of the Stratonovich-Weyl kernels is constructed explicitly. In the presented theory we use the concept of the generalized coherent states, that brings physical insight into the mathematical formalism.

REVTeX, 4 pages. More information on http://www.technion.ac.il/~brif/science.html

References in corpus (2)

• Algebras of distributions suitable for phase-space quantum mechanics. I
• Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra

Cited by in corpus (56)

• Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries
• Wigner functions, squeezing properties and slow decoherence of atomic Schrodinger cats
• Quantum dynamics in the bosonic Josephson junction
• Phase space simulation method for quantum computation with magic states on qubits
• Visualizing operators of coupled spin systems
• Continuous phase-space representations for finite-dimensional quantum states and their tomography
• Quasiprobability representation of quantum coherence
• A hidden variable model for universal quantum computation with magic states on qubits
• Orbital angular momentum in phase space
• Wigner tomography of multispin quantum states
• Quantization of the Optical Phase Space S^2 = {phi mod 2pi, I > 0} in Terms of the Group SO(1,2)
• Quantum polarization tomography of bright squeezed light
• Wigner-Weyl isomorphism for quantum mechanics on Lie groups
• Quasiprobability distributions for quantum-optical coherence and beyond
• SU(N)-symmetric quasi-probability distribution functions
• Discrete coherent and squeezed states of many-qudit systems
• Multipolar hierarchy of efficient quantum polarization measures
• Quantum phase-space representation for curved configuration spaces
• Rapid and slow decoherence in conjunction with dissipation in a system of two-level atoms
• Bopp operators and phase-space spin dynamics: Application to rotational quantum brownian motion
• Wigner distributions and quantum mechanics on Lie groups: the case of the regular representation
• Wigner function for SU(1,1)
• Metric Properties of the Fuzzy Sphere
• Quantum versus classical polarization states: when multipoles count
• Non-negative Wigner functions for orbital angular momentum states
• Wigner function for the orientation state
• Continuous phase spaces and the time evolution of spins: star products and spin-weighted spherical harmonics
• The role of cohomology in quantum computation with magic states
• Coherent States for Transparent Potentials
• Wigner distributions for non Abelian finite groups of odd order
• Time evolution of coupled spin systems in a generalized Wigner representation
• Quasistates and quasiprobabilities
• Fast computation of spherical phase-space functions of quantum many-body states
• Towards a complete, continuous, Wigner function for an ensemble of spins or qubits
• JIMWLK Evolution, Lindblad Equation and Quantum-Classical Correspondence
• On the family of Wigner functions for N-level quantum system
• Quantum speed limits in arbitrary phase spaces
• Exact variational dynamics of the multimode Bose-Hubbard model based on SU(M) coherent states
• Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
• Generalised coherent states and the diagonal representation for operators
• Phase space quantum-classical hybrid model
• Kenfack Zyczkowski indicator of nonclassicality for two non-equivalent representations of Wigner function of qutrit
• Orbital angular momentum from marginals of quadrature distributions
• Transition probabilities and transition rates in discrete phase space
• Non-adiabatic Ring Polymer Molecular Dynamics in the Phase Space of the SU(N) Lie Group
• Hidden variable model for quantum computation with magic states on qudits of any dimension
• Polytopes of Absolutely Wigner Bounded Spin States
• Star product and ordered moments of photon creation and annihilation operators
• The stellar decomposition of Gaussian quantum states
• Grand Unification of All Discrete Wigner Functions on $d\times d$ Phase Space
• Wigner function for twisted photons
• Phase-Space Methods for Many-Body Quantum Optics
• Symmetries and Wigner representations of operational theories
• Quantum information in Riemannian spaces
• Quantum and semiclassical dynamics as fluid theories where gauge matters
• On a Resolution of the Identity in Terms of Coherent States