Distinguishability in Random States, Eigenstates, and Gravity

Recently, there has been significant progress in solving the black hole information problem from explicit calculations of the entropy of Hawking radiation, confirming consistency of gravity with unitarity. One aspect of the information problem left unresolved by entropy calculations is the distinguishability of different black hole microstates: why do different microstates appear to lead to the same final (thermal) state? I will address this problem by studying the distinguishability of radiation coming from different black holes. In parallel, I will present a derivation of the subsystem eigenstate thermalization hypothesis for a class of chaotic many-body systems as well as generalizations to tensor network states.