Localizable quantum coherence

Highlights: • quantum coherence can be localized in subsystems of a composite system. • measurement aided localization is more efficient than tracing out. • by localizable coherence we can distinguish topological states or characterize localization transitions. • average localizable coherence in the Hilbert space is studied. Coherence is a fundamental notion in quantum mechanics, defined relative to a reference basis. As such, it does not necessarily reveal the locality of interactions nor takes into account the accessible operations in a composite quantum system. In this paper, we put forward a notion of localizable coherence as the coherence that can be stored in a particular subsystem, either by measuring or just by disregarding the rest. We examine its spreading, its average properties in the Hilbert space and show that it can be applied to reveal the real-space structure of states of interest in quantum many-body theory, for example, localized or topological states.