Superadditivity in large $N$ field theories and performance of quantum tasks

TL;DR

This paper explores superadditivity in large N field theories and holography, revealing how it enables probing black hole interiors and performing quantum tasks beyond naive expectations, with implications for quantum error correction.

Contribution

It demonstrates the role of superadditivity in holography, connecting algebraic structures to quantum task performance and proposing a generalized framework for connected wedge theorems.

Findings

Superadditive algebras can access black hole interiors.

Superadditivity explains quantum error correction success.

Rephrasing CWTs in terms of superadditivity suggests a broader equivalence.

Abstract

Field theories exhibit dramatic changes in the structure of their operator algebras in the limit where the number of local degrees of freedom ($N$) becomes infinite. An important example of this is that the algebras associated to local subregions may not be additively generated in the limit. We investigate examples and explore the consequences of this ``superadditivity'' phenomenon in large $N$ field theories and holographic systems. In holographic examples we find cases in which superadditive algebras can probe the black hole interior, while the additive algebra cannot. We also discuss how superaddivity explains the sucess of quantum error correction models of holography. Finally we demonstrate how superadditivity is intimately related to the ability of holographic field theories to perform quantum tasks that would naievely be impossible. We argue that the connected wedge theorems (CWTs) of May, Penington, Sorce, and Yoshida, which characterize holographic protocols for quantum tasks, can be re-phrased in terms of superadditive algebras and use this re-phrasing to conjecture a generalization of the CWTs that is an equivalence statement.