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On Density Operators with Gaussian Weyl Symbols

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Advances in Microlocal and Time-Frequency Analysis

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Abstract

The notion of reduced density operator plays a fundamental role in quantum mechanics where it is used as a tool to study statistical properties of subsystems. In the present work we review this notion rigorously from a mathematical perspective using pseudodifferential theory, and we give a new necessary and sufficient condition for a Gaussian density operator to be separable.

This paper is dedicated to Prof. Luigi Rodino for his 70th birthday

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Acknowledgements

This work has been financed by the Austrian Research Foundation FWF (Grant number P27773). It is our pleasure to thank a Referee for very useful remarks and for having pointed out inaccuracies in a first version of this work.

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Correspondence to Maurice A. de Gosson .

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de Gosson, M.A. (2020). On Density Operators with Gaussian Weyl Symbols. In: Boggiatto, P., et al. Advances in Microlocal and Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-36138-9_12

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