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Topological insulators combine insulating properties in the bulk withscattering-free transport along edges, supporting dissipationlessunidirectional energy and information flow even in the presence of defects anddisorder. The feasibility of engineering quantum Hamiltonians with photonictools, combined with the availability of entangled photons, raises theintriguing possibility of employing topologically protected entangled states inoptical quantum computing and information processing. However, while two-photonstates built as a product of two topologically protected single-photon statesinherit full protection from their single-photon "parents", high degree ofnon-separability may lead to rapid deterioration of the two-photon states afterpropagation through disorder. We identify physical mechanisms which contributeto the vulnerability of entangled states in topological photonic lattices andpresent clear guidelines for maximizing entanglement without sacrificingtopological protection.

Two-photon edge states in photonic topological insulators: topological protection versus degree of entanglement