Stabilizer dimension of graph states
D. H. Zhang, Heng Fan, Di Zhou · Physical Review A · 2009
The entanglement properties of a multiparty pure state are invariant under local unitary transformations. The stabilizer dimension of a multiparty pure state characterizes how many types of such local unitary transformations exist for the state. We find that the stabilizer dimension of an $n$-qubit $(n\ensuremath{\ge}2)$ graph state is associated with three specific configurations in its graph. We further show that the stabilizer dimension of an $n$-qubit $(n\ensuremath{\ge}3)$ graph state is equal to the degree of irreducible two-qubit correlations in the state.