Asymptotic Fate of Continuously Monitored Quantum Systems

by Finn Schmolke (Universität Stuttgart)

Wednesday Oct 15, 2025, 11:00 AM → 12:00 PM Europe/Paris

Katherine Johnson (1R3)

In this talk, we highlight some aspects of the asymptotic behavior of quantum systems subject to random fluctuations. We first show that classical white noise can induce quantum synchronization in spin-chains of arbitrary length. However, synchronization induced by classical noise emerges only on average over the ensemble of noise realizations while 'single shot' synchronization on the level of individual realizations would be more desirable. By contrast, quantum noise, induced by continuous measurement, has a more dramatic impact on quantum evolution. Measurement-induced synchronization is indeed possible but emerges only as a special case of a more general phenomenon: quantum trajectories spontaneously undergo irreversible localization transitions and get trapped in a fraction of the available state space.

Thus striving for a complete characterization of the asymptotic behavior of continuously monitored quantum systems, we find that localization can be either complete, where the strongest possible confinement is achieved, or incomplete, where localization terminates prematurely. We explore the necessary and sufficient conditions for incomplete localization, which turn out to be determined by the trajectories' ability to 'distinguish' between different regions of the Hilbert space. Based these findings, we argue that continuous measurement can be interpreted simply as a prolonged projective measurement, that comes equipped with a generalized Born rule. We finally comment on numerical procedures to identify the most fine-grained resolution of the Hilbert space structure without requiring prior knowledge of symmetries.