  Based on a proposed coherence measure, we show that the local coherence of a
bipartite quantum pure state (coherence of its reduced density matrix) is
exactly the same as the minimal average co- herence with all potential
pure-state realizations under consideration. In particular, it is shown that
bipartite concurrence of pure states just captures the maximal difference
between local coherence and the average coherence of one subsystem induced by
local operations on the other subsystem with the assistance of classical
communications, which provides an alternative operational meaning for bipartite
concurrence of pure states. The relation between concurrence and the proposed
coherence measure can also be extended to bipartite mixed states.
