A Quantum Information View on Black Holes

Abstract

A major discovery by Hawking was that the interplay between general relativity and quantum theory leads to the prediction that black holes must radiate. In Hawking’s original calculation however, the black hole radiation was found to be of thermal character, thus leaving behind a mixed state describing the radiation as soon as the black hole has fully evaporated. This conclusion stands in apparent contradiction to the reversibility of time evolution in quantum theory which predicts a pure final state of the radiation, thereby giving rise to the famous black hole information puzzle. This discrepancy can be more concretely illustrated in terms of (von Neumann) entropy: Hawking’s prediction leads to a continuously increasing entropy during the black hole evaporation while quantum theory instead dictates that the entropy should decrease in the final stages of the evaporation.

In analyzing this puzzle, it turns out that information-theoretic tools allow us to interpret the different behaviours of the black hole radiation entropy during evaporation. In this talk, I will focus on the notion of typicality and discuss a random unitary model for black hole evaporation, providing us with a clue whether and how fast information that fell into the black hole may be recovered.

References

• https://arxiv.org/pdf/0708.4025.pdf (Hayden, Preskill)
• https://arxiv.org/abs/2110.14653 (Renner, Wang)