Positivity of quantum discord is shown to be equivalent to the strong sub additivity of the von Neumann entropy. This leads to a connection between the mother protocol of quantum information theory and quantum discord. We exploit this to show that 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 discord to be a measure of coherence in these protocols. Our work generalizes an earlier operational interpretation of discord provided in terms of quantum state merging.
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