Quantum information processing and composite quantum fields

• Main Authors: Sanjaye Ramgoolam, Michal Sedlák
• Format: Article
• Language: English
• Published: SpringerOpen 2019-01-01
• Series: Journal of High Energy Physics
• Subjects: 1/N Expansion; AdS-CFT Correspondence
• Online Access: http://link.springer.com/article/10.1007/JHEP01(2019)170

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.