Wigner distributions for finite dimensional quantum systems: An algebraic approach

Abstract

We discuss questions pertaining to the definition of `momentum', `momentum space', `phase space', and `Wigner distributions'; for finite dimensional quantum systems. For such systems, where traditional concepts of `momenta' established for continuum situations offer little help, we propose a physically reasonable and mathematically tangible definition and use it for the purpose of setting up Wigner distributions in a purely algebraic manner. It is found that the point of view adopted here is limited to odd dimensional systems only. The mathematical reasons which force this situation are examined in detail.

Latex, 13 pages

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• Coherence makes quantum systems 'magical'
• Wigner distributions for finite state systems without redundant phase point operators
• From the discrete Weyl -- Wigner formalism for symmetric ordering to a number -- phase Wigner function
• Harnessing quantumness of states using discrete Wigner functions under (non)-Markovian quantum channels
• Unitary and Non-Unitary Matrices as a Source of Different Bases of Operators Acting on Hilbert Spaces
• Stokes vector and its relationship to Discrete Wigner Functions of multiphoton states
• Discrete Wigner-Weyl calculus for the finite lattice
• Spin flip of multiqubit states in discrete phase space