Quantum Zeno and Anti-Zeno Responses: Universal Spectral Criterion for Measurement-Induced Decay

Abstract:We develop a general framework for characterizing the response of an evolving quantum system to repetitive quantum measurements. Modeling each evolution-measurement cycle as a quantum channel induced by an effective Liouvillian generator, we find that the Liouvillian spectral gap determines the measurement-induced decay rate. We analyze how the spectral gap responds to the measurement frequency, and define a quantum Zeno response as a decrease in the gap with increasing measurement frequency, and an anti-Zeno response as the opposite. We illustrate this criterion for both discrete-time and continuous-time quantum measurements. In an exactly solvable discrete-time qubit model, the exceptional-point spectral coalescence or spectral crossings mark the transition between Zeno and anti-Zeno responses, which can be experimentally distinguished from the long-time decay envelope of the survival probability. In a continuous-time superconducting-qubit defect model, the same transition manifests as smooth extrema of the spectral gap. Our results establish a universal spectral criterion for measurement-induced decay, offering a practical route to identify and manipulate these effects in generic quantum systems.

arXiv:2608.20702 [quant-ph]

(or arXiv:2608.20702v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.20702 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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