Quantum-Theoretic Modeling in Computer Science: A Complex Hilbert Space Model for Entangled Concepts in Corpuses of Documents

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.