Quantum Information Processing and Composite Quantum Fields

TL;DR

This paper provides a representation theoretic proof of identities involving Young diagram hook contents, connecting quantum information processing, combinatorics, and quantum field theory with implications for AdS/CFT.

Contribution

It introduces a new representation theoretic proof of identities and generalizations, linking quantum information, combinatorics, and quantum field theory through permutation centralizer algebras.

Findings

Identities involving hook contents of Young diagrams are proven using trace identities.

Connections between quantum information tasks and composite quantum fields are discussed.

Implications for AdS/CFT correspondence are explored.

Abstract

Some beautiful identities involving hook contents of Young diagrams have been found in the field of quantum information processing, along with a combinatorial proof. We here give a representation theoretic proof of these identities and a number of generalizations. Our proof is based on trace identities for elements belonging to a class of permutation centralizer algebras. These algebras have been found to underlie the combinatorics of composite gauge invariant operators in quantum field theory, with applications in the AdS/CFT correspondence. Based on these algebras, we discuss some analogies between quantum information processing tasks and the combinatorics of composite quantum fields and argue that this can be fruitful interface between quantum information and quantum field theory, with implications for AdS/CFT.