Quantum-theoretic Modeling in Computer Science A complex Hilbert space model for entangled concepts in corpuses of documents
This provides a confirmation of quantum structures in document analysis, similar to findings in human cognition, but is incremental as it applies an existing entanglement scheme to new data.
The authors tackled the problem of modeling concept co-occurrences in document corpora using quantum theory, showing that the data violated the CHSH inequality, indicating entanglement between combined concepts with a strong form involving both states and measurements.
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 the Bell 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 occurrence 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.