On Density Operators with Gaussian Weyl Symbols

  • Maurice A. de GossonEmail author
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


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 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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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Faculty of Mathematics (NuHAG)University of ViennaWienAustria

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