Detecting two dimensional symmetry protected topological order in a ground state wave function

Symmetry protected topological states cannot be deformed to a trivial state so long as the symmetry is preserved, yet there is no local order parameter that can distinguish them from a trivial state. We demonstrate how to detect whether a two dimensional ground state has symmetry protected topological order; the measurement play a similar role as the topological entanglement entropy does for detecting anyons. For finite abelian symmetries the measurement gives a complete characterization of the 3rd cohomology class that describes the order. The proposed measurement is validated numerically for a model with $Z_2$ symmetry protected order.