Perfect State Transfer on NEPS of the path P3

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.