Detection of long-range entanglement in gapped quantum spin liquids by local measurements

Topological order, reflected in long-range patterns of entanglement, is quantified by the topological entanglement entropy gamma. We show that for gapped quantum spin liquids it is possible to extract gamma using two-spin local correlators. We demonstrate our method for the gapped Z(2) Kitaev spin liquid on a honeycomb lattice with anisotropic interactions. We show that the gamma = ln 2 for Z(2) topological order can be simply extracted from local two-spin correlators across two different bonds that involve only Majorana fermions, with an accuracy comparable to or higher than the Kitaev-Preskill construction. This implies that even though the ground state can be factorized into the product of Majorana and gauge sectors, the different superselection sectors of Z(2) gauge theory determined by global Wilson loop operators can be reflected locally in the Majorana sector.