Information recovery in the Hayden-Preskill protocol

We revisit information retrieval from evaporating black holes in the Hayden-Preskill protocol, treating the black hole dynamics as Haar-random. We compute, down to the first exponentially suppressed terms, all integer-indexed R\'enyi mutual informations between a black hole, its radiation, and a reference that catalogues Alice's diaries. We find that dropping a diary into a young black hole effectively delays the Page time. We also compute the radiation : diary reflected R\'enyi entropies, and identify a technical reason why they cannot be continued to the reflected entropy by the replica trick.