Reusability of Quantum Catalysts

Quantum catalysts enable transformations that otherwise would be forbidden, offering a pathway to surpass conventional limits in quantum information processing. Among them, embezzling catalysts stand out for achieving near-perfect performance while tolerating only minimal disturbance, bridging the gap between ideal and practical catalysis. Yet, this superior capability comes at a cost: Each use slightly degrades the catalyst, leading to an inevitable accumulation of imperfection. This gradual decay defines their most distinctive property - reusability - which, despite its fundamental importance, remains largely unexplored. Here, we establish a quantitative framework to characterize the operational lifetime of embezzling catalysts, focusing on their role in entanglement distillation and extending the analysis to quantum teleportation. We show that the catalytic advantage inevitably diminishes with repeated use, deriving bounds on the maximum effective reuse rounds for a desired performance gain. Our results uncover the finite reusability of catalysts in quantum processes and point toward sustainable strategies for quantum communication.