Quantum Fractional Revival in Unitary Cayley Graphs

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.