Pretty good quantum state transfer in asymmetric graphs via potential

TL;DR

This paper demonstrates that adding potentials to asymmetric graphs can induce pretty good quantum state transfer between specific nodes, extending previous results from symmetric graphs to a broader class.

Contribution

It introduces a method to achieve pretty good state transfer in asymmetric graphs by adding potentials, generalizing prior work limited to symmetric graphs with involution.

Findings

Pretty good state transfer can be induced in asymmetric graphs.

Adding potentials enables asymptotically perfect state transfer.

The method generalizes previous symmetric graph results.

Abstract

We construct infinite families of graphs in which pretty good state transfer can be induced by adding a potential to the nodes of the graph (i.e. adding a number to a diagonal entry of the adjacency matrix). Indeed, we show that given any graph with a pair of cospectral nodes, a simple modification of the graph, along with a suitable potential, yields pretty good state transfer (i.e. asymptotically perfect state transfer) between the nodes. This generalizes previous work, concerning graphs with an involution, to asymmetric graphs.