  Quantum coherence quantifies the amount of superposition a quantum state can
have in a given basis. Since there is a difference in the structure of
eigenstates of the ergodic and many-body localized systems, we expect them also
to differ in terms of their coherences in a given basis. Here, we numerically
calculate different measures of quantum coherence in the excited eigenstates of
an interacting disordered Hamiltonian as a function of the disorder. We show
that quantum coherence can be used as an order parameter to detect the
well-studied ergodic to many-body-localized phase transition. We also perform
quantum quench studies to distinguish the behavior of coherence in thermalized
and localized phases. We then present a protocol to calculate measurement-based
localizable coherence to investigate the thermal and many-body localized
phases. The protocol allows one to investigate quantum correlations
experimentally in a non-destructive way, in contrast to measures that require
tracing out a subsystem, which always destroys coherence and correlation.
