Global Coherence in Quantum Discord as a Resource

This work addresses which aspect of $\mathit{\text{bipartite}}\mathit{\text{coherence}}$ in $\mathit{\text{quantum}}\mathit{\text{discord}}$ is essential for $\mathit{\text{genuinely}}\mathit{\text{quantum}}\mathit{\text{correlation}}$. To this end, $\mathit{\text{global}}\mathit{\text{coherence}}$ 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 $\mathit{\text{global}}\mathit{\text{coherence}}$ as $\mathit{\text{a}}\mathit{\text{resource}}$, $\mathit{\text{any}}\mathit{\text{local}}\mathit{\text{operations}}$ of the form ${\mathrm{\Phi }}_A\otimes {\mathrm{\Phi }}_B$, which may create coherence locally, are $\mathit{\text{free}}\mathit{\text{operations}}$. This implies that with global coherence as a resource for operational tasks, any local operations can be freely used, but require $\mathit{\text{classical}}\mathit{\text{randomness}}\mathit{\text{not}}\mathit{\text{to}}\mathit{\text{be}}\mathit{\text{freely}}$ available. Using this identification, we demonstrate that $\mathit{\text{global}}\mathit{\text{coherence}}$ is a $\mathit{\text{necessary}}\mathit{\text{resource}}$ for the task of $\mathit{\text{semi-device-independent}}\mathit{\text{steerability}}$ of quantum discord. On the other hand, for the task of $\mathit{\text{remote}}\mathit{\text{state}}\mathit{\text{preparation}}$ using $\mathit{\text{quantum}}\mathit{\text{discord}}$ in two-qubit states, a $\mathit{\text{necessary}}\mathit{\text{and}}\mathit{\text{sufficient}}\mathit{\text{quantum}}\mathit{\text{resource}}$ is identified by invoking a $\mathit{\text{witness}}\mathit{\text{of}}\mathit{\text{global}}\mathit{\text{coherence}}$.