  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. Importantly, identification of
modes inside the horizon with radiation modes (i.e., large scale nonlocality
across the horizon) is not required to provide a physical picture of unitary
evaporation. Radiation modes can encode the interior information while still
remaining independent degrees of freedom.
