arXiv:quant-ph/0507094quant-ph
Wigner distributions for finite dimensional quantum systems: An algebraic approach
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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.
Wigner Functions are great and all, but they work quite badly for finite dimensional systems. Specifically they are a bit complicated for odd dimensional systems and don't work at all for even dimensional systems (see e.g. [1]). Given their limited applicability I don't see why…
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