Celestial Quantum Error Correction II: From Qudits to Celestial CFT

TL;DR

This paper develops a quantum error correction framework for celestial CFTs describing asymptotically flat spacetimes, incorporating vacuum degeneracies and IR divergences, and introduces a continuum limit with celestial symmetries and GKP codes.

Contribution

It introduces a novel QEC framework for celestial CFTs that encodes vacuum degeneracies and IR effects, using a continuum limit of qudit chains and celestial symmetries.

Findings

Finite N qudit chain exhibits celestial symmetries and GKP codes.

Continuum limit yields states with quantized BMS hair.

Framework leverages $w_{1+ abla}$ hierarchy and twistor space sigma models.

Abstract

A holographic CFT description of asymptotically flat spacetimes inherits vacuum degeneracies and IR divergences from its gravitational dual. We devise a Quantum Error Correcting (QEC) framework to encode both effects as correctable fluctuations on the CFT dual. The framework is physically motivated by embedding a chain of qudits in the so-called Klein spacetime and then taking a continuum $N\to \infty$ limit. At finite $N$ the qudit chain 1) enjoys a discrete version of celestial symmetries and 2) supports a Gottesman-Kitaev-Preskill (GKP) code. The limit results in hard states with quantized BMS hair in the celestial torus forming the logical subspace, robust under errors induced by soft radiation. Technically, the construction leverages the recently studied $w_{1+\infty}$ hierarchy of soft currents and its realization from a sigma model in twistor space.