Reusability of Quantum Catalysts

TL;DR

This paper develops a quantitative framework to analyze the reusability and operational lifetime of embezzling quantum catalysts, revealing their finite reusability limits in quantum information tasks.

Contribution

It introduces a new framework to quantify the reusability of quantum catalysts, specifically embezzling catalysts, in quantum information processing.

Findings

Reusability of quantum catalysts diminishes with each use.

Bounds on maximum reuse rounds for desired performance are derived.

Finite reusability impacts strategies for sustainable quantum communication.

Abstract

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.