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