Abstract
In this article, we give characterization for the existence of quantum fractional revival in unitary Cayley graph utilizing adjacency matrix Hamiltonian. Unitary Cayley graph \(X=(Z_{n},S)\) is a special graph as connection set \(S\subseteq Z_{n}\) is the collection of coprimes to \(n\) . Unitary Cayley graph is an integral graph and its adjacency matrix is a circulant one. We prove that quantum fractional revival in unitary Cayley graphs exists only when the number of vertices is even. Number-theoretic and spectral characterizations are given for unitary Cayley graph admitting quantum fractional revival. Quantum fractional revival is analogous to quantum entanglement and can be useful in quantum communication.
