量子纠错和大$N$
Quantum error correction and large $N$
摘要：
近年来，量子纠错（QEC）已成为AdS/CFT的重要组成部分。不幸的是，没有场论的论点来解释为什么QEC在已知的全息系统中成立。本文的目的是通过研究各种大$N$理论的费米子扇区的纠错性质来填补这一空白。具体来说，我们研究$SU(N)$矩阵量子力学和3秩张量$O(N)^3$理论。这两个理论都包含大规范群。我们认为，规范单态确实形成了量子纠错码。我们的考虑是纯粹基于大的$N$分析，并不呼吁一个特定形式的哈密顿量或全息。
英文摘要：
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.
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