Hawking radiation and the quantum marginal problem

by Erik Aurell (KTH)

Thursday 2 Dec 2021, 13:00 → 14:00 Europe/Stockholm

AlbaNova C4:3059 - Café Planck (AlbaNova Main Building)

In two famous papers almost half a century ago, Hawking found that black holes radiate as black bodies with temperature inversely proportional to the black hole mass. The sum of the entropies of all the modes of Hawking radiation is far larger than what could have been the entropy of an astrophysical object which gave rise to the black hole. As an extreme thought experiment one can imagine that object to have been in a pure quantum state, in which case a pure state would have developed into a mixed state, which is not allowed in quantum mechanics. 

The favored resolution of the above "black hole information paradox" in the recent literature is that in some way information is eventually encoded in quantum correlations among the modes of the radiation. How that happens (or if it happens) is however not known.

Here I will show that there is a connection to the quantum marginal problem in quantum information theory. In its Gaussian version this theory gives explicit constraints on the mode temperatures which have to be satisfied if the total state is to be pure. Those constraints are not difficult to satisfy for large black holes which emit very many Hawking particles, but are also rather forgiving for holes of initially small mass. I will pose the extension of the standard quantum marginal problem if also two-mode marginals are given, and what a solution to that more difficult problem could tell us about the Hawking evaporation process. 

The talk is based on joint work with Michał Eckstein and Paweł Horodecki, available as [arXiv:2012.14418]