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arXiv:quant-ph/0504210 · Physica A Statistical Mechanics and its Applications

Wigner function for discrete phase space: Exorcising ghost images

Arturo Argüelles, Thomas Dittrich

Published Jun 10, 2005• 20 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2005.05.015

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The general Weyl–Wigner formalism in finite dimensional phase spaces is investigated. Then this formalism is specified to the case of symmetric ordering of operators in an odd-dimensional Hilbert space. A respective Wigner function on the discrete phase space is found and the limit, when the dimension of Hilbert space tends to infinity, is considered. It is shown that this limit gives the number–phase Wigner function in quantum optics. Analogous results for the “almost” symmetric ordering in an even-dimensional Hilbert space are obtained. Relations between the discrete Wigner functions introduced in our paper and some other discrete Wigner functions appearing in literature are studied.