2021/03/09 by Charlyne de Gosson, Maurice A. de Gosson, de Gosson, Charlyne +1
Mathematics · #advanced mathematical theories #Mathematical Analysis and Transform Methods #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2103.05605
It is standard to assume that the Wigner distribution of a mixed quantum\nstate consisting of square-integrable functions is a quasi-probability\ndistribution, that is that its integral is one and that the marginal properties\nare satisfied. However this is in general not true. We introduce a class of\nquantum states for which this property is satisfied, these states are dubbed\n"Feichtinger states" because they are defined in terms of a class of functional\nspaces (modulation spaces) introduced in the 1980's by H. Feichtinger. The\nproperties of these states are studied, which gives us the opportunity to prove\nan extension to the general case of a result of Jaynes on the non-uniqueness of\nthe statistical ensemble generating a density operator. As a bonus we obtain a\nresult for convex sums of Wigner transforms.\n