An Operator Algebraic Approach To Black Hole Information

TL;DR

This paper introduces an operator algebraic framework for understanding black hole information recovery, utilizing von Neumann algebras, Jones index theory, and quantum teleportation analogies to model the evaporation and information retrieval process.

Contribution

It develops a novel operator algebraic approach to black hole information, connecting quantum teleportation, spacetime translation, and algebraic structures in black hole physics.

Findings

Operator algebraic description of information recovery in black holes.

Use of Jones index theory and type II$_1$ subfactors.

Interpretation of spacetime translation as quantum teleportation.

Abstract

We present an operator algebraic perspective on the black hole information problem. For a black hole after Page time that is entangled with the early radiation we formulate a version of the information puzzle that is well-posed in the $G\to 0$ limit. We then give a description of the information recovery protocol in terms of von Neumann algebras using elements of the Jones index theory of type II$_1$ subfactors. The subsequent evaporation and recovery steps are represented by Jones's basic construction, and an operation called the canonical shift. A central element in our description is the Jones projection, which leads to an entanglement swap and implements an operator algebraic version of a quantum teleportation protocol. These aspects are further elaborated on in a microscopic model based on type I algebras. Finally, we argue that in the emergent type III algebra the canonical shift may be interpreted as a spacetime translation and, hence, that at the microscopic level "translation = teleportation".