The black hole information paradox revolves around the question whether the formation of a black hole, its emission of Hawking radiation and finally its evaporation are to be described by a unitary process, or not. Central to this problem is the question whether the total quantum state of all emitted radiation can be pure, or not. In the work I present, we show that restoring unitarity and a pure total state after evaporation does not require strong quantum entanglement between any pair of Hawking modes. To this end, we introduce a new method to the study of random Gaussian states: We consider the family of $N$-mode pure Gaussian states whose marginals are thermal states. This set of states can be shown to be compact and equipped with a natural measure induced from the Haar measure of the symplectic group. This enables us to find the probability distribution over correlations between two modes. The derived expressions for the distribution of mode-mode correlations in random, pure, Gaussian states with given marginals, are general and should be interesting to many areas beyond black hole physics.
(While following up on an earlier seminar on this work in December, this talk will be complementary and self-contained.)
- E. Aurell, L. Hackl, P. Horodecki, R. H. Jonsson, and M. Kieburg, “Random pure Gaussian states and Hawking radiation.” arXiv.2311.10562.