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

• URL: http://arxiv.org/abs/2103.05605v4
• Date: Sat, 21 Aug 2021 17:13:19 GMT
• Title: On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution
• Authors: Charlyne de Gosson and Maurice de Gosson
• Abstract summary: It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution. We introduce a class of quantum states for which this property is satisfied. These states are dubbed "Feichtinger states" because they are defined in terms of a class of functional spaces.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, that is that its integral is one and that the marginal properties are satisfied. However this is in general not true. We introduce a class of quantum states for which this property is satisfied, these states are dubbed "Feichtinger states" because they are defined in terms of a class of functional spaces (modulation spaces) introduced in the 1980's by H. Feichtinger. The properties of these states are studied, which gives us the opportunity to prove an extension to the general case of a result of Jaynes on the non-uniqueness of the statistical ensemble generating a density operator. As a bonus we obtain a result for convex sums of Wigner transforms.

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