We generalize the quantum CUSUM (QUSUM) algorithm for quickest change-point
detection, analyzed in finite dimensions by Fanizza, Hirche, and Calsamiglia
(Phys. Rev. Lett. 131, 020602, 2023), to infinite-dimensional quantum systems.
Our analysis relies on a novel generalization of a result by Hayashi (Hayashi,
J. Phys. A: Math. Gen. 34, 3413, 2001) concerning the asymptotics of quantum
relative entropy, which we establish for the infinite-dimensional setting. This
enables us to prove that the QUSUM strategy retains its asymptotic optimality,
characterized by the relationship between the expected detection delay and the
average false alarm time for any pair of states with finite relative entropy.
Consequently, our findings apply broadly, including continuous-variable systems
(e.g., Gaussian states), facilitating the development of optimal change-point
detection schemes in quantum optics and other physical platforms, and rendering
experimental verification feasible.

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