All States are Universal Catalysts in Quantum Thermodynamics

Abstract

Quantum catalysis is a fascinating concept that demonstrates how 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, it has been 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 multicopy 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; 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 multicopy form nor a very-large-dimension catalyst is required to activate most allowed transformations catalytically.