Monotones in General Resource Theories

Tomáš Gonda(Perimeter Institute), Robert Spekkens (Perimeter Institute)

A central problem in the study of resource theories is to find functions that are nonincreasing under resource conversions—termed monotones—in order to quantify resourcefulness. Various constructions of monotones appear in many different concrete resource theories. How general are these constructions? What are the necessary conditions we need in order to be able to apply them? To answer these questions, we introduce several general ways to construct monotones and show how standard constructions arise as special cases of these. These constructions also provide methods for defining new interesting monotones in any resource theory of interest.