We discuss recent applications of Euclidean path integrals
to the black hole information problem. In calculations with replica
wormholes as the next-to-leading order correction to the
Gibbons-Hawking saddlepoint, the radiation density matrix approaches a
pure state at late times, following the Page curve. We compare unitary
evaporation of black holes (in real time), mediated by calculable
quantum hair effects, with the replica wormhole results. Both replica
wormhole and quantum hair approaches imply that radiation states are
macroscopic superpositions of spacetime backgrounds, invalidating
firewall and monogamy of entanglement constructions.