Relative Phase Shifts for Metaplectic Isotopies Acting on Mixed Gaussian States

TL;DR

This paper investigates the relative phase shift in mixed quantum systems, specifically focusing on Gaussian states under metaplectic isotopies, and enhances the theoretical framework involving the Conley-Zehnder index.

Contribution

It generalizes previous results on phase shifts for Gaussian states and provides rigorous proofs, enriching the theoretical understanding of quantum phase phenomena.

Findings

Extended the theory of phase shifts for mixed Gaussian states

Provided rigorous proofs for previous conjectures

Connected phase shifts with the Conley-Zehnder index

Abstract

We address in this paper the notion of relative phase shift for mixed quantum systems. We study the Pancharatnam-Sjoeqvist phase shift for metaplectic isotopies acting on Gaussian mixed states. We complete and generalize previous results obtained by one of us while giving rigorous proofs. This gives us the opportunity to review and complement the theory of the Conley-Zehnder index which plays an essential role in the determination of phase shifts.