Quantum error correction and large $N$

TL;DR

This paper investigates the error correcting properties of large N gauge theories, providing field-theoretic insights into quantum error correction in holographic systems without relying on specific Hamiltonians.

Contribution

It demonstrates that gauge singlet states in large N theories form quantum error correcting codes through purely large N analysis, filling a gap in understanding holographic QEC.

Findings

Gauge singlet states form quantum error correcting codes

Analysis applies to SU(N) matrix and tensor theories

Results are derived without specific Hamiltonian assumptions

Abstract

In recent years quantum error correction(QEC) has become an important part of AdS/CFT. Unfortunately, there are no field-theoretic arguments about why QEC holds in known holographic systems. The purpose of this paper is to fill this gap by studying the error correcting properties of the fermionic sector of various large $N$ theories. Specifically we examine $SU(N)$ matrix quantum mechanics and 3-rank tensor $O(N)^3$ theories. Both of these theories contain large gauge groups. We argue that gauge singlet states indeed form a quantum error correcting code. Our considerations are based purely on large $N$ analysis and do not appeal to a particular form of Hamiltonian or holography.