Toy Gravizap for Black Hole Redemption

TL;DR

This paper presents a topological model of quantum teleportation as an analogy for information transfer in black hole evaporation, linking entanglement dynamics to the concept of islands and entropy evolution.

Contribution

It introduces a toy topological realization of quantum teleportation to model information transfer in black hole physics, connecting entanglement, entropy, and the island paradigm.

Findings

Topological realization of quantum teleportation for black hole models

Analog of the Page curve for Hawking radiation entropy

Identification of interior regions encoding exterior information

Abstract

In this note we discuss a topological realization of the quantum teleportation protocol. Such a realization facilitates keeping track of the evolution of quantum correlations in the system. It is then suggested, that an implementation of a similar protocol can serve as a toy model of a process of information transfer between causally disconnected regions, such as the one that should take place in a unitary evolution of a quantum black hole. Hawking quanta provide the necessary entangled pairs for the teleportation channel, and the same interaction mechanism that creates the Hawking pairs, destroys the entanglement at the late stages of the evolution. Different steps of the teleportation protocol are characterized by the entropies associated with the disconnected regions, and one can introduce an analog of the Page curve for the entropy of the Hawking radiation. Some regions of the ``black hole'' interior appear to actually encode the information of the exterior, so it is natural to identify them with the ``islands'' of the semiclassical gravity analysis.