Perfect State Transfer on NEPS of the path P3

TL;DR

This paper investigates the conditions under which NEPS graphs constructed from the path P3 exhibit perfect state transfer, expanding the class of graphs known to have this property in quantum communication.

Contribution

It provides a sufficient condition for NEPS of P3 to have perfect state transfer and constructs new such graphs, including connected ones for various parameters.

Findings

Identifies a sufficient condition for NEPS of P3 to exhibit perfect state transfer.

Constructs new graphs with perfect state transfer using NEPS.

Proves existence of connected NEPS graphs with perfect state transfer for certain parameters.

Abstract

Perfect state transfer is significant in quantum communication networks. There are very few graphs having this property. So, it is useful to find some new graphs having perfect state transfer. A good way to construct new graphs is by forming NEPS. It is known that the graph $P_{3}$ exhibits perfect state transfer and so we investigate some NEPS of the path $P_{3}$. A sufficient condition is found for a NEPS of $P_{3}$ to have perfect state transfer. Using these NEPS, some other graphs are constructed having perfect state transfer. We also prove that for every $n\in \Nl\setminus \left\lbrace 1\right\rbrace$ and any odd positive integer $k< n$, there is a basis $\Omega$ such that $NEPS(P_{3},\ldots, P_{3};\Omega)$ is connected and exhibits perfect state transfer.