Global Coherence in Quantum Discord as a Resource
arXiv:2410.04430
Abstract
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 , 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}.
16 pages, 3 figures; over all presentation has been modified over the version v4; a measure of global coherence introduced and its connection to the measure of coherence of single-partite states is addressed