Nonlocal advantage of quantum coherence in high-dimensional states

By local measurements on party $A$ of a system $\mathit{AB}$ and classical communication between its two parties, one can achieve a nonlocal advantage of quantum coherence (NAQC) on party $B$. For the ${l}_{1}$ 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 ($d\ifmmode\times\else\texttimes\fi{}d$)-dimensional states when $d$ is a power of a prime. We also presented a framework for formulating NAQC and showed through explicit examples its capacity for 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.