Estimating time in quantum chaotic systems and black holes

by Dr Shreya Vardhan (Stanford University)

Wednesday 4 Dec 2024, 11:00 → 12:00 Asia/Kolkata

AG (80)

A time-evolved pure state in a unitary chaotic quantum many-body system macroscopically resembles a thermal density matrix. However, while a thermal density matrix does not evolve with time, a pure state undergoing unitary evolution must continue to evolve with time unless it is an energy eigenstate. We sharpen this difference by considering an information-theoretic task where we attempt to estimate the time for which the state has been evolved by making measurements on the state. We quantify the effectiveness of the time estimate using a quantity from quantum metrology called the quantum Fisher information. This quantity shows an interesting interplay between expectations from thermalization and constraints from unitarity. By treating evaporating black holes as examples of chaotic systems, we come to the conclusion that the ability to make local time estimates using the radiation is very poor before the Page time, and suddenly improves after the Page time.