  In quantum information theory there is a construction for quantum channels,
appropriately called a quantum graph, that generalizes the confusability graph
construction for classical channels in classical information theory. In this
paper, we provide a definition of connectedness for quantum graphs that
generalizes the classical definition. This is used to prove a quantum version
of a particular case of the classical tree-packing theorem from graph theory.
Generalizations for the related notions of $k$-connectedness and of orthogonal
representation are also proposed for quantum graphs, and it is shown that
orthogonal representations have the same implications for connectedness as they
do in the classical case.
