  An amply regular graph is a regular graph such that any two adjacent vertices
have $\alpha$ common neighbors and any two vertices with distance $2$ have
$\beta$ common neighbors. We prove a sharp lower bound estimate for the
Lin--Lu--Yau curvature of any amply regular graph with girth $3$ and
$\beta>\alpha$. The proof involves new ideas relating discrete Ricci curvature
with local matching properties: This includes a novel construction of a regular
bipartite graph from the local structure and related distance estimates. As a
consequence, we obtain sharp diameter and eigenvalue bounds for amply regular
graphs.
