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Quantum Information and Black Holes

One of the most important problems in physics is finding a theory that can completely describe both quantum mechanics and gravity. The most prominent physical example of a system where quantum fields meet strong gravitational fields is near black holes. One of the first and most important studies of quantum field theory around black holes is Hawking’s paper [1] showing that, under some reasonable assumptions about the nature of quantum gravity, black holes should give off radiation, leading to their eventual evaporation. This result prompted an intense discussion on how to deal with quantum information in the vicinity of a black hole that persists to this day. The purpose of this report is to highlight some interesting connections between the fields of black hole physics and quantum information theory. We start by discussing the seemingly simple problem of whether it is possible to recover quantum information that falls into a black hole. To facilitate this discussion, we describe some physics results about what happens to the infalling radiation and how it interacts with the Hawking radiation that the black hole emits. This is done in Section 2. Section 3 then describes how Hayden and Preskill [2] transformed the way physicists think about this problem by casting it into the terms of quantum computing as a task of unscrambling quantum information, and presents their argument that this task is information-theoretically possible. We then present in Section 4 a more recent result from Kitaev and Yoshida [3] that describes an algorithm to solve this computational problem. Our discussion then pivots to an example of how quantum information theory can lead to surprising new physics and give us valuable insight into the nature of quantum gravity. We begin this discussion in Section 5 by summarizing the AMPS firewall paradox [4]. In Section 6 we describe how Hayden and Harlow [5] were able to avoid this paradox using quantum information theory. Section 7 ends with a brief discussion of the current situation in the firewall paradox debate.