Record Loss Sets a Rare-Trajectory Limit on Quantum Purification

Abstract:Continuous quantum feedback uses time-resolved measurement records to steer monitored systems toward pure states. Yet how the information available to a controller determines the ultimate purification speed remains unresolved. We establish this relation for a qubit under fixed-spectrum Hermitian monitoring with detector loss, obtaining the exact long-time impurity-moment spectrum optimized over causal basis controls at each horizon. Rare records with nearly canceled evidence then make all moments from half order upward decay at the Bhattacharyya information rate between two quantum nondemolition record laws. Aligned quantum nondemolition monitoring preserves that binary distinguishability and attains the limit, while complete detection restores an order-dependent branch. The mechanism extends to higher dimensions, where an attainable rank-two ceiling lies above the full-rank qutrit upper bound over a finite moment interval, establishing retained record distinguishability as a purification resource.

arXiv:2607.09118 [quant-ph]

(or arXiv:2607.09118v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.09118 Focus to learn more arXiv-issued DOI via DataCite

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