Quantum Fractional Revival on Graphs

TL;DR

This paper investigates the spectral conditions under which graphs exhibit fractional revival, a quantum phenomenon relevant for entanglement, providing characterizations for paths and cycles and linking it to other quantum transport phenomena.

Contribution

It offers necessary and sufficient spectral conditions for fractional revival in graphs, especially paths and cycles, connecting it to existing quantum transport concepts.

Findings

Characterization of fractional revival in paths and cycles

Spectral conditions for fractional revival in graphs

Connection between fractional revival, state transfer, and mixing

Abstract

Fractional revival is a quantum transport phenomenon important for entanglement generation in spin networks. This takes place whenever a continuous-time quantum walk maps the characteristic vector of a vertex to a superposition of the characteristic vectors of a subset of vertices containing the initial vertex. A main focus will be on the case when the subset has two vertices. We explore necessary and sufficient spectral conditions for graphs to exhibit fractional revival. This provides a characterization of fractional revival in paths and cycles. Our work builds upon the algebraic machinery developed for related quantum transport phenomena such as state transfer and mixing, and it reveals a fundamental connection between them.