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Superadditivity in large $N$ field theories and performance of quantum tasks
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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.
Forward citations
Cited by 4 Pith papers
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The Making of von Neumann Algebras from Bulk Focusing
A boundary region's infinite-N operator algebra is a von Neumann algebra exactly when its generalized causal wedge closes on the same region; null geodesic focusing is the bulk mechanism.
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Disjoint additivity and local quantum physics
Local quantum systems should obey disjoint additivity plus Haag duality, a combination that survives higher-form symmetries and fails for known nonlocal constructions.
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Volume as an index of a subalgebra
Proposes that the exponential of the maximal volume slice in AdS equals the index of inclusion of boundary subalgebras, but the supplied text is an unrelated astrochemistry paper.
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Learning shadows to predict quantum ground state correlations
The manuscript body does not match the claimed paper: the abstract promises a shadow-tomography ground-state scheme, while the text is the Leutheusser-Liu preprint on bulk volume and subalgebra indices.
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