Catalytic channels are the only noise-robust catalytic processes

TL;DR

The paper establishes that robust catalysis is feasible only through catalytic channels and is generally constrained by the composition rules of the underlying resource theory. It proves a broad no-go: in completely resource non-generating theories with minimal composition, robust catalysis and resource broadcasting are impossible, while certain maximal/separable compositions can permit robust catalytic advantages in specific theories such as local athermality, characterized by single resource monotones like $F_{\max}$. The authors develop two key tools: (i) a formal equivalence between robust catalysis and resource broadcasting, and (ii) a compositional framework using minimal/maximal/affine/separable constructions to determine when robust catalytic channels can appear. They further analyze strict catalysis, show no extra advantage with full-rank catalysts, and explore battery-assisted transformations, outlining practical conditions under which robust catalytic benefits can be realized. The work thereby clarifies the prospects and limits of catalytic advantages across entanglement, coherence, thermodynamics, magic, and imaginarity, guiding future experiments and theory toward catalysis in non-CRNG regimes and channel-centric approaches.

Abstract

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.

Figures (2)

• Figure 1: Illustrations of noisy catalysis. The top-left quadrant depicts the ideal scenario, where a catalyst $\tau$ facilitates a state transformation from $\rho$ into $\rho'$ and is returned exactly to its initial state. The top-right quadrant represents robust catalysis, where the catalyst state remains unaffected despite errors in the system state preparation. The bottom quadrants show how other sources of errors (catalyst state preparation and channel implementation) impact the final states.
• Figure 2: The logical relationship between the existence of robust catalysis (RC) and resource broadcasting (RB). The two-way relationship between RC and RB for completely resource non-generatic (CRNG) theories is shown by Thm. \ref{['thm:broadcast_robcat']}. For non-CRNG theories, broadcasting implies robust catalysis, but not the other way around.

Theorems & Definitions (19)

• Theorem 1
• Theorem 2
• Theorem 3
• Example 1: Accumulating errors on the catalyst
• Lemma 4
• proof
• Theorem 5: Ref. Piani2009MRelEnt, Thm. 1
• Theorem 6
• proof
• Theorem 7