Global Coherence in Quantum Discord as a Resource

TL;DR

This paper investigates the role of global coherence as a fundamental resource in quantum discord, establishing its necessity for tasks like steerability and remote state preparation, and clarifying the operational significance of bipartite coherence.

Contribution

It introduces the concept of global coherence as a nonlocal coherence resource and links it to quantum discord, providing a framework for understanding quantum correlations in operational tasks.

Findings

Global coherence is a necessary resource for semi-device-independent steerability.

Global coherence is essential for remote state preparation using quantum discord.

Local operations can be free if they do not require additional classical randomness.

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}.