  Topological insulators combine insulating properties in the bulk with
scattering-free transport along edges, supporting dissipationless
unidirectional energy and information flow even in the presence of defects and
disorder. The feasibility of engineering quantum Hamiltonians with photonic
tools, combined with the availability of entangled photons, raises the
intriguing possibility of employing topologically protected entangled states in
optical quantum computing and information processing. However, while two-photon
states built as a product of two topologically protected single-photon states
inherit full protection from their single-photon "parents", high degree of
non-separability may lead to rapid deterioration of the two-photon states after
propagation through disorder. We identify physical mechanisms which contribute
to the vulnerability of entangled states in topological photonic lattices and
present clear guidelines for maximizing entanglement without sacrificing
topological protection.
