IQI Weekly Seminar

Abstract: We consider a macroscopic black hole past its Page time. If the black hole dynamics is described by a rapidly scrambling unitary operation, then it must generate an unusual form of entanglement between an outgoing Hawking mode and earlier radiation. This entanglement is protected, in that it is unaffected by a large class of perturbations applied to the early radiation. We conceive a firewall-like experiment, in which an external observer perturbs the early radiation, jumps into the black hole, and measures the effect of the perturbation on the entanglement by performing a fixed measurement. We prove that, if a variant of the Harlow-Hayden decoding task is computationally hard, no observer with a size significantly smaller than the black hole can drastically alter the measurement outcome. The maximum influence, quantified in terms of the change in the measurement statistics, is exponentially small in the black hole entropy. We argue the computational hardness of the task based on the hardness of inverting an injective one-way function.