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arXiv · 1706.06171

On the Positivity of Trace Class Operators

Elena Cordero·Maurice de Gosson·Fabio Nicola
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Abstract

The characterization of positivity properties of Weyl operators is a notoriously difficult problem, and not much progress has been made since the pioneering work of Kastler, Loupias, and Miracle-Sole (KLM). In this paper we begin by reviewing and giving simpler proofs of some known results for trace-class Weyl operators; the latter play an essential role in quantum mechanics. We then apply time-frequency analysis techniques to prove a phase space version of the KLM condition; the main tools are Gabor frames and the Wigner formalism. Finally, discrete approximations of the KLM condition, which are tractable numerically, are provided.

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Elena Cordero, Maurice de Gosson, Fabio Nicola. 2017-06-19. On the Positivity of Trace Class Operators. https://arxiv.org/abs/1706.06171

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