SLOCC-Equivalence of Pure States and Graph States

Measurement-based quantum computation (MBQC) is a model of quantum computing allowing for information processing by means of adaptive local measurements on a resource state. This resource state is a massively entangled many-body state, the best known example of which is the cluster state. While the cluster is not itself a non-degenerate ground state of a realistic Hamiltonian, other resources that are equivalent to the cluster under stochastic local operations and classical communication (SLOCC) may be. We describe a protocol for determining SLOCC-equivalence between arbitrary pure states and graph states, a generalization of cluster states.