Relative phase shifts for metaplectic isotopies acting on mixed Gaussian states

We address in this paper the notion of relative phase shift for mixed quantum systems. We study the Pancharatnam–Sjöqvist phase shift φ(t)=ArgTr(U^tρ^) for metaplectic isotopies acting on Gaussian mixed states. We complete and generalize the previous results obtained by one of us, while giving rigor...

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Bibliographic Details
Published in:Journal of mathematical physics 2018-05, Vol.59 (5)
Main Authors: de Gosson, Maurice A., Nicacio, Fernando
Format: Article
Language:English
Subjects:
Isotopes
Mathematical analysis
Normal distribution
Phase shift
Quantum physics
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Summary:We address in this paper the notion of relative phase shift for mixed quantum systems. We study the Pancharatnam–Sjöqvist phase shift φ(t)=ArgTr(U^tρ^) for metaplectic isotopies acting on Gaussian mixed states. We complete and generalize the previous results obtained by one of us, while giving rigorous proofs. The key actor in this study is the theory of the Conley–Zehnder index which is an intersection index related to the Maslov index.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5026586