Abstract
By local measurements on party A of a system AB and classical communication between its two parties, one can achieve a nonlocal advantage of quantum coherence (NAQC) on party B. For the l₁ norm of coherence and the relative entropy of coherence, we generalized the framework of NAQC for two qubits and derived the criteria which capture NAQC in the (d× d)-dimensional states when d is a power of a prime. We also presented a new framework for formulating NAQC, and showed through explicit examples its capacity on capturing the NAQC states. Moreover, we proved that any bipartite state with NAQC is quantum entangled, thus the obtained criteria can also be used as an entanglement witness.