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arXiv · 2410.04430

Global Coherence in Quantum Discord as a Resource

Chellasamy Jebarathinam·Huan-Yu Ku·Hao-Chung Cheng·Hsi-Sheng Goan
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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 $\Phi_A \otimes \Phi_B$, 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}.

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Chellasamy Jebarathinam, Huan-Yu Ku, Hao-Chung Cheng, Hsi-Sheng Goan. 2024-10-06. Global Coherence in Quantum Discord as a Resource. https://arxiv.org/abs/2410.04430

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