Set Coherence: Basis-Independent Quantification of Quantum Coherence

The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can, however, lifted considering sets states. Here we introduce the concept set for characterizing systems in basis-independent way. We construct measures quantifying states as well measurements. These feature operational meaning terms discrimination games and capture precisely advantage offered by given over incoherent ones. Along way, also connect notion various resource-theoretic approaches recently developed systems.