Holographic spacetime, black holes and quantum error correcting codes: A review

TL;DR

This review explores how holographic principles, quantum error correction, and tensor networks contribute to understanding bulk spacetime reconstruction, black hole microstates, and the Page curve in quantum gravity.

Contribution

It synthesizes recent advances in holography, quantum error correction, and microstate models, offering new perspectives on black hole information and spacetime emergence.

Findings

Quantum error correction frameworks enable bulk reconstruction.

Tensor network toy models illustrate operator algebra resolution.

Microstate models shed light on black hole complementarity.

Abstract

This article reviews the progress in our understanding of the reconstruction of the bulk spacetime in the holographic correspondence from the dual field theory including an account of how these developments have led to the reproduction of the Page curve of the Hawking radiation from black holes. We review quantum error correction and relevant recovery maps with toy examples based on tensor networks, and discuss how it provides the desired framework for bulk reconstruction in which apparent inconsistencies with properties of the operator algebra in the dual field theory are naturally resolved. The importance of understanding the modular flow in the dual field theory has been emphasized. We discuss how the state-dependence of reconstruction of black hole microstates can be formulated in the framework of quantum error correction with inputs from extremal surfaces along with a quantification of the complexity of encoding of bulk operators. Finally, we motivate and discuss a class of tractable microstate models of black holes which can illuminate how the black hole complementarity principle can emerge operationally without encountering information paradoxes, and provide new insights into generation of desirable features of encoding into the Hawking radiation.