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arXiv · 2408.13083

Functional calculus of quantum channels for the holomorphic discrete series of $SU(1,1)$

Robin van Haastrecht
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Abstract

The tensor product of two holomorphic discrete series representations of $SU(1,1)$ can be decomposed as a direct sum of infinitely many discrete series. I shall introduce equivariant quantum channels for each component of the direct sum, mapping bounded operators on one factor of the tensor product to operators on the component. Next I prove a limit formula for the trace of the functional calculus and I prove that the limit can be expressed using generalized Husimi functions or using Berezin transforms.

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BibTeXRIS

Robin van Haastrecht. 2024-08-23. Functional calculus of quantum channels for the holomorphic discrete series of $SU(1,1)$. https://arxiv.org/abs/2408.13083

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