  We initiate the study of approximate quantum fractional revival in graphs, a
generalization of pretty good quantum state transfer in graphs. We give a
complete characterization of approximate fractional revival in a graph in terms
of the eigenvalues and eigenvectors of the adjacency matrix of a graph. This
characterization follows from a lemma due to Kronecker on Diophantine
approximation, and is similar to the spectral characterization of pretty good
state transfer in graphs. Using this, we give a complete characterizations of
when approximate fractional revival can occur in paths and in cycles.
