  We consider 1d Hamiltonian systems whose ground states display symmetry
protected topological order. We show that ground states within the topological
phase cannot be connected with each other through LOCC between a bipartition of
the system. Our claim is demonstrated by analyzing the entanglement spectrum
and Renyi entropies of different physical systems providing examples for
symmetry protected topological phases. Specifically, we consider spin-1/2
Cluster-Ising model and a class of spin-1 models undergoing quantum phase
transitions to the Haldane phase. Our results provide a probe for
simmetry-protected topological order, that holds true even at the system's
local scale. Therefore our analysis can serve as as local experimental test for
topological order.
