  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.
