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It is standard to assume that the Wigner distribution of a mixed quantumstate consisting of square-integrable functions is a quasi-probabilitydistribution, that is that its integral is one and that the marginal propertiesare satisfied. However this is in general not true. We introduce a class ofquantum states for which this property is satisfied, these states are dubbed"Feichtinger states" because they are defined in terms of a class of functionalspaces (modulation spaces) introduced in the 1980's by H. Feichtinger. Theproperties of these states are studied, which gives us the opportunity to provean extension to the general case of a result of Jaynes on the non-uniqueness ofthe statistical ensemble generating a density operator. As a bonus we obtain aresult for convex sums of Wigner transforms.

On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution