A complete classification of perfect state transfer in Grover walks on abelian Cayley graphs
The study completely classifies connected Cayley graphs over finite abelian groups that show perfect state transfer in Grover walks. It proves that such graphs can only have valencies of 1, 2, or 4. For valency four, it provides a specific condition on the connection set S. The results extend previous classifications to all abelian groups and all possible valencies.