Onkar Parrikar

On the stabilizer complexity of Hawking radiation - (virtual)

We will study the complexity of Hawking radiation for an evaporating black hole from the perspective of the stabilizer theory of quantum computation. Specifically, we will calculate Wigner negativity -- a magic monotone which can be interpreted as a measure of the stabilizer complexity, or equivalently, the complexity of classical simulation -- in various toy models for evaporating black holes. We will first calculate the Wigner negativity of Hawking radiation in the PSSY model directly using the gravitational path integral, and show that the negativity is $O(1)$ before the Page transition, but becomes exponentially large past the Page transition. We will also derive a universal, information theoretic formula for the negativity which interpolates between the two extremes. We will then study the Wigner negativity in a dynamical model of black hole evaporation. In this case, the negativity shows a sharp spike at early times resulting from the coupling between the black hole and radiation bath, but at late times when the system settles down, the negativity satisfies the same universal formula as in the PSSY msodel. Finally, we will also propose a formula for Wigner negativity in general holographic states satisfying the Ryu-Takayanagi formula for entanglement entropy. We will argue that a python's lunch region in the entanglement wedge implies a stabilizer complexity which is exponentially large in the gap between the entropies corresponding to the outermost and minimal extremal surfaces.