Hierarchy of the nonlocal advantage of quantum coherence and Bell nonlocality

TL;DR

This paper establishes a hierarchy between the nonlocal advantage of quantum coherence and Bell nonlocality, showing that NAQC captures stronger quantum correlations and proposing a measure for quantifying NAQC in bipartite states.

Contribution

It proves a strict hierarchy between NAQC and Bell nonlocality for certain states and provides numerical evidence that this hierarchy extends generally, introducing a measure for NAQC.

Findings

NAQC captures stronger quantum correlations than Bell nonlocality.

NAQC states form a subset of Bell nonlocality states.

Proposed a quantitative measure for NAQC.

Abstract

Quantum coherence and nonlocality capture nature of quantumness from different aspects. For the two-qubit states with diagonal correlation matrix, we prove strictly a hierarchy between the nonlocal advantage of quantum coherence (NAQC) and Bell nonlocality by showing geometrically that the NAQC created on one qubit by local measurement on another qubit captures quantum correlation which is stronger than Bell nonlocality. For general states, our numerical results present strong evidence that this hierarchy may still hold. So the NAQC states form a subset of the states that can exhibit Bell nonlocality. We further propose a measure of NAQC that can be used for a quantitative study of it in bipartite states.