Topological protection versus degree of entanglement of two-photon light

The possibility of implementing quantum Hamiltonians using linear optical systems and entangled photons has opened the door to employing topologically protected entangled states in optical quantum information processing. In two-dimmensional photonic topologial insulators, single photon edge-states inhabit in the gap between the energy bands supporting the bulk states. Breaking the topological protection requires disorder with sufficient strength to close such a bandgap. For states comprising two indistinguishable photons, the same bandgap does not exists. The reason is because when a linear optical system is excited by two indistinguishable photons, all possible two-photon eigenstates are given by the symmetric combinations of the single-photon eigenstates. Consequently, the corresponding two-photon eigenvalues are given by the combinations of the single-photon eigenvaues λ (2) = λ m + λ n . This fundamental additive property of the single photon eigenenergies removes the bandgap and leads to massive degeneracies of the edge-edge, edge-bulk, and bulk-bulk two-photon states.