Fractional revival on non-cospectral vertices

TL;DR

This paper introduces an infinite family of unweighted graphs exhibiting fractional revival between non-cospectral vertices, expanding understanding of quantum information transfer in networks beyond perfect state transfer limitations.

Contribution

It provides the first known examples of unweighted graphs with fractional revival between non-cospectral vertices and overlapping pairs, addressing gaps in quantum network theory.

Findings

Constructed an infinite family of graphs with fractional revival between non-cospectral vertices.

Presented examples of unweighted graphs with overlapping fractional revival pairs.

Extended the theoretical understanding of quantum state transfer in complex networks.

Abstract

Perfect state transfer and fractional revival can be used to move information between pairs of vertices in a quantum network. While perfect state transfer has received a lot of attention, fractional revival is newer and less studied. One problem is to determine the differences between perfect state transfer and fractional revival. If perfect state transfer occurs between two vertices in a graph, the vertices must be cospectral. Further if there is perfect state transfer between vertices $a$ and $b$ in a graph, there cannot be perfect state transfer from $a$ to any other vertex. No examples of unweighted graphs with fractional revival between non-cospectral vertices were known; here we give an infinite family of such graphs. No examples of unweighted graphs where the pairs involved in fractional revival overlapped were known; we give examples of such graphs as well.