Purification of quantum trajectories in infinite dimensions

• URL: http://arxiv.org/abs/2509.13377v1
• Date: Tue, 16 Sep 2025 07:20:11 GMT
• Title: Purification of quantum trajectories in infinite dimensions
• Authors: Federico Girotti, Alessandro Vitale,
• Abstract summary: We show that purification of quantum trajectories in terms of 'dark' subspaces fails to hold in infinite dimensional ones.<n>We prove that the new phenomenon emerging in our class of models and preventing purification to happen is the only new possibility that emerges in infinite dimensional systems.
• Score: 46.43084711486819
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work we exhibit a class of examples that show that the characterization of purification of quantum trajectories in terms of 'dark' subspaces that was proved for finite dimensional systems fails to hold in infinite dimensional ones. Moreover, we prove that the new phenomenon emerging in our class of models and preventing purification to happen is the only new possibility that emerges in infinite dimensional systems. Our proof strategy points out that the emergence of new phenomena in infinite dimensional systems is due to the fact that the set of orthogonal projections is not sequentially compact. Having in mind this insight, we are able to prove that the finite dimensional extends to a class of infinite dimensional models.

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