Aspect of bipartite coherence in quantum discord to semi-device-independent nonlocality and its implication for quantum information processing

Abstract: $\textit{Nonlocality}$ or $\textit{steerability}$ of $\textit{quantum discord}$ can be demonstrated in the context of a $\textit{semi-device-independent}$ Bell or steering scenario where shared randomness is not a free resource, respectively. This work addresses which aspect of $\textit{bipartite coherence}$ is essential for such semi-device-independent quantum information tasks going beyond Bell nonlocality or standard quantum steering. It has been shown that $\textit{global coherence}$ of a single system can be transformed into $\textit{bipartite entanglement}$. However, global coherence can also be present in quantum discord. At the same time, discord can display bipartite coherence locally, i.e., only in a subsystem or in both subsystems. Thus, global coherence of bipartite separable states is defined here as a form of bipartite coherence that is not reducible to local coherence in any of the subsystems or both subsystems. To answer the above-mentioned question, we demonstrate that global coherence is necessary to demonstrate semi-device-independent nonlocality or steerability of quantum discord in any given Bell or steering scenario, respectively. From this result, it follows that for the resource theory of semi-device-independent nonlocality or steerability of discord, any $\textit{local operations}$ of the form $\Phi_A \otimes \Phi_B$ that may create $\textit{coherence locally}$ from an incoherent state are $\textit{free operations}$. As a by-product, we identify the precise quantum resource for the quantum communication task of $\textit{remote state preparation}$ using two-qubit separable states.