Fluctuations in the entropy of Hawking radiation and interior information recovery

Recent study revealed that the inclusion of Euclidean wormhole into the gravitational path integral renders the entropy of Hawking radiation consistent with unitarity, deriving the Page curve of the Hawking radiation. On the other hand, since the gravitational path integral with Euclidean wormhole computes quantities of ensemble average of theories, it is possible that the entropy of Hawking radiation of each gravity theory fluctuate wildly around the ensemble average. In this talk we show that such fluctuation is as small as the dimension of the system, ensuring the answer from the ensemble average is typical. We also study information recovery from the black hole interior which is also known to be possible after the Page time. We again find that the recovery is also typical, by studying information theoretic quantities of the encoding map as well as directly examining the entanglement fidelity of the Petz recovery map.