Hierarchy of the nonlocal advantage of quantum coherence and Bell nonlocality

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