We report on the first example of quantum coherence between the spins of muons and quadrupolar nuclei. We observe this effect in vanadium intermetallic compounds which adopt the A15 crystal structure, and whose members include all technologically dominant superconductors. The entangled states are extremely sensitive to the local structural and electronic environments through the electric field gradient at the quadrupolar nuclei. This case-study demonstrates that positive muons can be used as a quantum sensing tool to probe also structural and charge related phenomena in materials, even in the absence of magnetic order. The data here contained can be used to reproduce all results and graphs shown in the article.