Quantum-Theoretic Modeling in Computer Science

A Complex Hilbert Space Model for Entangled Concepts in Corpuses of Documents
  • Diederik Aerts
  • Lester Beltran
  • Suzette Geriente
  • Sandro SozzoEmail author


We work out a quantum-theoretic model in complex Hilbert space of a recently performed test on co-occurrencies of two concepts and their combination in retrieval processes on specific corpuses of documents. The test violated the Clauser-Horne-Shimony-Holt version of Bell’s inequalities (‘CHSH inequality’), thus indicating the presence of entanglement between the combined concepts. We make use of a recently elaborated ‘entanglement scheme’ and represent the collected data in the tensor product of Hilbert spaces of the individual concepts, showing that the identified violation is due to the presence of a strong form of entanglement, involving both states and measurements and reflecting the meaning connection between the component concepts. These results provide a significant confirmation of the presence of quantum structures in corpuses of documents, like it is the case for the entanglement identified in human cognition.


CHSH inequality Quantum entanglement Quantum structures Corpuses of documents Natural language processing 



This work was supported by QUARTZ (Quantum Information Access and Retrieval Theory), the Marie Skłodowska-Curie Innovative Training Network 721321 of the European Union’s Horizon 2020 research and innovation programme.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Diederik Aerts
    • 1
  • Lester Beltran
    • 1
  • Suzette Geriente
    • 1
  • Sandro Sozzo
    • 2
    Email author
  1. 1.Center Leo Apostel (Clea)Free University of Brussels (VUB)BrusselBelgium
  2. 2.School of Business and Centre IQSCSUniversity of LeicesterLeicesterUK

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