  Positivity of quantum discord is shown to be equivalent to the strong sub
additivity of the Von-Nuemann entropy. This leads to a connection between the
mother protocol of quantum information theory [A. Abeyesinghe, I. Devetak, P.
Hayden, and A. Winter, Proc. R. Soc. A 465, 2537, (2009)] and quantum discord.
We exploit this to show that quantum discord is a measure coherence in the
performance of the mother protocol. Since the mother protocol is a unification
of an important class of problems (those that are bipartite, unidirectional and
memoryless), we show quantum discord to be a measure of coherence in these
protocols. Our work generalizes an earlier operational interpretation of
quantum discord provided in terms of quantum state merging [V. Madhok and A.
Datta, Phys. Rev. A 83, 032323, (2011)].
