Non-local computation and the black hole interior

In a two sided black hole, systems falling in from opposite asymptotic regions can meet inside the black hole and interact. This is the case even while the two CFTs describing each asymptotic region are non-interacting. Here, we relate these behind the horizon interactions to non-local quantum computations. This gives a quantum circuit perspective on these interactions, which applies whenever the interaction occurs in the past of a certain extremal surface that sits inside the black hole and in arbitrary dimension. Whenever our perspective applies, we obtain a boundary signature for these interior collisions which is stated in terms of the mutual information. We further revisit the connection discussed earlier between bulk interactions in one sided AdS geometries and non-local computation, and recycle some of our techniques to offer a new perspective on making that connection precise.