Catalytic channels are the only noise-robust catalytic processes

Catalysis refers to the possibility of enabling otherwise inaccessible quantum state transitions by supplying an auxiliary system, provided that the auxiliary is returned to its initial state at the end of the protocol. We show that previous studies on catalysis are largely impractical, because even small errors in the system’s initial state can irreversibly degrade the catalyst. To overcome this limitation, we introduce robust catalytic transformations and explore the fundamental extent of their capabilities. We demonstrate that robust catalysis is closely tied to the property of resource broadcasting. In particular, in completely resource non-generating theories, robust catalysis is possible if and only if resource broadcasting is possible. We develop a no-go theorem under a set of general axioms, demonstrating that robust catalysis is unattainable for a broad class of quantum resource theories. However, surprisingly, we also identify thermodynamical scenarios where maximal robust catalytic advantage can be achieved. Our approach clarifies the practical prospects of catalytic advantage for a wide range of quantum resources, including entanglement, coherence, thermodynamics, magic, and imaginarity.

💡 Research Summary

The paper revisits quantum catalytic transformations from a practical standpoint, focusing on the impact of realistic preparation noise. A catalytic process traditionally enables a state transition ρ → ρ′ by coupling the system to an auxiliary catalyst τ, which must be returned exactly to its original state after the operation. Earlier works assumed ideal, noise‑free conditions; however, any experimental implementation inevitably suffers from small errors ε in preparing the input state. Such errors accumulate over repeated uses, potentially degrading the catalyst linearly with the number of repetitions, while errors in catalyst preparation itself are one‑off and bounded by the data‑processing inequality.

To address this, the authors introduce robust catalytic transformations. A transformation is called robust against ε‑level preparation noise if, for every system state σ satisfying ‖σ − ρ‖₁ ≤ ε, the catalyst is recovered exactly after the joint channel Λ acts on σ ⊗ τ. The robustness parameter ε can be arbitrarily small, reflecting the desire for exact catalyst preservation even under infinitesimal input imperfections.

The central technical result, termed the Central Fact, shows that robustness forces the underlying joint channel Λ to be a catalytic channel. A catalytic channel is defined as the reduced map ˜Λ(·)=Tr_C