Connectivity for quantum graphs

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 a definition of connectedness for quantum graphs is provided, which generalizes the classical definition. It is shown that several examples of well-known quantum graphs (quantum Hamming cubes and quantum expanders) are connected. A quantum version of a particular case of the classical tree-packing theorem from Graph Theory is also proved. 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.