Finite-size catalysis in quantum resource theories

TL;DR

This paper investigates finite-size quantum catalysis, establishing conditions for practical catalytic transformations, revealing catalytic resonance phenomena, and illustrating applications in entanglement and thermodynamics resource theories.

Contribution

It introduces finite-size conditions for catalytic transformations, connecting them to multi-copy processes and uncovering catalytic resonance effects for resource-efficient quantum transformations.

Findings

Finite-size catalysts enable practical quantum transformations.

Catalytic resonance reduces catalyst dimension requirements.

Applications demonstrated in entanglement and thermodynamics theories.

Abstract

Quantum catalysis, the ability to enable previously impossible transformations by using auxiliary systems without degrading them, has emerged as a powerful tool in various resource theories. Although catalytically enabled state transformations have been formally characterized by the monotonic behaviour of entropic quantifiers (e.g., the von Neumann entropy or non-equilibrium free energy), such characterizations often rely on unphysical assumptions, namely the ability of using catalysts of infinitely large dimension. This approach offers very limited insights into the practical significance of using catalysis for quantum information processing. Here, we address this problem across a broad class of quantum resource theories. Leveraging quantum information tools beyond the asymptotic regime, we establish sufficient conditions for the existence of catalytic transformations with finite-size catalysts. We further unveil connections between finite-size catalysis and multi-copy transformations. Notably, we discover a phenomenon of catalytic resonance: by carefully tailoring the catalysts's state, one can drastically reduce the required dimension of the catalyst, thus enabling efficient catalytic transformations with minimal resources. Finally, we illustrate our findings with examples from the resource theories of entanglement and thermodynamics, as well in the context of catalytic unitary transformations.