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Quantum information processing and composite quantum fields

Journal of High Energy Physics volume 2019, Article number: 170 (2019) Cite this article

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.

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Affiliations

  1. Centre for Research in String Theory, Department of Physics, Queen Mary University of London, Mile End Road, London, E1 4NS, U.K.

    Sanjaye Ramgoolam

  2. National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical Physics, University of the Witwatersrand, Wits, 2050, South Africa

    Sanjaye Ramgoolam

  3. RCQI, Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, 84511, Bratislava, Slovakia

    Michal Sedlák

  4. Faculty of Informatics, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic

    Michal Sedlák

Authors
  1. Sanjaye Ramgoolam
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  2. Michal Sedlák
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Correspondence to Sanjaye Ramgoolam.

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ArXiv ePrint: 1809.05156

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Ramgoolam, S., Sedlák, M. Quantum information processing and composite quantum fields. J. High Energ. Phys. 2019, 170 (2019). https://doi.org/10.1007/JHEP01(2019)170

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Keywords

  • 1/N Expansion
  • AdS-CFT Correspondence