Let $X$ be a finite, simple, undirected graph on a set $V$ of $n$ vertices with adjacency matrix $A$. In the theory of quantum information, many recent papers have explored the continuous time evolution of an $n$-state quantum system with time-dependent evolution operator $U(t)=e^{iAt}$. We say $X$ exhibits perfect state transfer from $b$ to $c$ at time $\tau$ if $U(\tau)_{a,b}=0$ for all $a\neq c$. Given that perfect state transfer (in this sense) is rare, it is natural to look for weaker conditions. For $S,T\subseteq V$ and $\tau \in \mathbb{R}$, we say $X$ has $(S,T)$-group state transfer at time $\tau$ if $U(\tau)_{a,b}=0$ whenever $b\in S$ and $a\not\in T$. This is obviously a generalisation of perfect state transfer, but also a generalisation of fractional revival. In this talk, we provide examples as well as a basic theory of group state transfer.

This talk is based on joint work with Luke C.~Brown, Drexel University, and Duncan Wright, Worcester Polytechnic Institute.