Quantum fractional revival governed by adjacency matrix Hamiltonian in unitary Cayley graphs

2024/10/04 by Soni, Rachana, Choudhary, Neelam, Singh, Navneet Pratap
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2410.03310

Abstract

In this article, we give characterization for 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 ⊆ 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. It is one of qubit state transfer phenomena useful in communication of quantum information.

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