This work addresses which aspect of \textit{ bipartite coherence} in \textit{ quantum discord} is essential for \textit{ genuinely quantum correlation}. To this end, \textit{ global coherence} of bipartite states is defined as a form of bipartite coherence that is not local coherence in either of the subsystems or in both subsystems alone, and we identify it as being indicated by a witness of discord. With \textit{ global coherence} as \textit{ a resource}, \textit{ any local operations} of the form $\Phi_A \otimes \Phi_B$, which may create coherence locally, are \textit{ free operations}. This implies that with global coherence as a resource for operational tasks, any local operations can be freely used, but require \textit{ classical randomness not to be freely} available. Using this identification, we demonstrate that \textit{ global coherence} is a \textit{ necessary resource} for the task of \textit{ semi-device-independent steerability} of quantum discord. On the other hand, for the task of \textit{ remote state preparation} using \textit{ quantum discord} in two-qubit states, a \textit{ necessary and sufficient quantum resource} is identified by invoking a \textit{ witness of global coherence}.
Categories: quant-ph