All states are universal catalysts in quantum thermodynamics

TL;DR

This paper proves that in quantum thermodynamics, all multi-copy states can serve as catalysts for any allowed transformation, simplifying the requirements for catalytic processes in resource theories.

Contribution

It reveals that any state, when provided in sufficient copies, can act as a catalyst for all transformations in majorization-governed resource theories, including quantum thermodynamics.

Findings

All resourceful states are catalysts for all allowed transformations.

Any state with enough copies can serve as a catalyst, no fine-tuning needed.

Numerical results suggest large or multi-copy catalysts are not necessary for most transformations.

Abstract

Quantum catalysis is a fascinating concept which demonstrates that certain transformations can only become possible when given access to a specific resource that has to be returned unaffected. It was first discovered in the context of entanglement theory and since then applied in a number of resource-theoretic frameworks, including quantum thermodynamics. Although in that case the necessary (and sometimes also sufficient) conditions on the existence of a catalyst are known, almost nothing is known about the precise form of the catalyst state required by the transformation. In particular, it is not clear whether it has to have some special properties or be finely tuned to the desired transformation. In this work we describe a surprising property of multi-copy states: we show that in resource theories governed by majorization all resourceful states are catalysts for all allowed transformations. In quantum thermodynamics this means that the so-called "second laws of thermodynamics" do not require a fine-tuned catalyst but rather any state, given sufficiently many copies, can serve as a useful catalyst. These analytic results are accompanied by several numerical investigations that indicate that neither a multi-copy form nor a very large dimension catalyst are required to activate most allowed transformations catalytically.