Quantum resource theories in the single-shot regime

One of the main goals of any resource theory such as entanglement, quantum\nthermodynamics, quantum coherence, and asymmetry, is to find necessary and\nsufficient conditions (NSC) that determine whether one resource can be\nconverted to another by the set of free operations. Here we find such NSC for a\nlarge class of quantum resource theories which we call affine resource theories\n(ART). ARTs include the resource theories of athermality, asymmetry, and\ncoherence, but not entanglement. Remarkably, the NSC can be expressed as a\nfamily of inequalities between resource monotones (quantifiers) that are given\nin terms of the conditional min entropy. The set of free operations is taken to\nbe (1) the maximal set (i.e. consists of all resource non-generating (RNG)\nquantum channels) or (2) the self-dual set of free operations (i.e. consists of\nall RNG maps for which the dual map is also RNG). As an example, we apply our\nresults to quantum thermodynamics with Gibbs preserving operations, and several\nother ARTs. Finally, we discuss the applications of these results to resource\ntheories that are not affine, and along the way, provide the NSC that a quantum\nresource theory consists of a resource destroying map.\n