  Nonlocal advantage of quantum coherence (NAQC) based on coherence
complementarity relations is generally viewed as a stronger nonclassical
correlation than Bell nonlocality. An arbitrary two-qubit state with NAQC must
be an entangled state, which demonstrates that the criterion of NAQC can also
be regarded as an entanglement witness. In this paper, we experimentally
investigate the NAQC for Bell-diagonal states with high fidelity in an
optics-based platform. We perform local measurements on a subsystem in three
mutually unbiased bases and reconstruct the density matrices of the measured
states by quantum state tomography process. By analyzing characteristic of the
$l_1$ norm, relative entropy and skew information of coherence with parameters
of quantum states, NAQC for the quantum states is accurately captured, and it
shows that our experimental results are well compatible with the theoretical
predictions. It is worth mentioning that quantum states with NAQC would have
higher entanglement, and thus NAQC could be expected to be a kind of useful
physical resource for quantum information processing.
