  We analyze a basis-independent definition of quantum coherence. The maximally
mixed state is used as the reference state, which allows for a way of defining
coherence that is invariant under arbitrary unitary transformations. The
basis-independent approach is applied to finding the distri- bution of the
coherence within a multipartite system, where the contributions due to
correlations between the subsystems and within each subsystem are isolated. The
use of the square root of the Jensen-Shannon divergence allows for inequality
relations to be derived between these quantities, giving a geometrical picture
within the Hilbert space of the system. We describe the relationship between
the basis-independent and the basis-dependent approaches, and argue that many
advan- tages exist for the former method. The formalism is illustrated with
several numerical examples which show that the states can be characterized in a
simple and effective manner.
