Entanglement in Cognition: Violating Bell Inequalities Beyond Cirel'son's Bound

We present the results of two tests where a sample of human participants were asked to make judgements about the conceptual combinations The Animal Acts and The Animal eats the Food. Both tests significantly violate the Clauser-Horne-Shimony-Holt version of Bell inequalities (‘CHSH inequality’), thus exhibiting manifestly non-classical behaviour due to the meaning connection between the individual concepts that are combined. We then apply a quantum-theoretical framework which we developed for any Bell-type situation and represent empirical data in complex Hilbert space. We show that the observed violations of the CHSH inequality can be explained as a consequence of a strong form of ‘quantum entanglement’ between the component conceptual entities in which both the state and measurements are entangled. We finally observe that a quantum model in Hilbert space can be elaborated in these Bell-type situations even when the CHSH violation exceeds the known ‘Cirel’son bound’, in contrast to widespread beliefs. These findings confirm and strengthen the results we recently obtained in a variety of cognitive tests and document and image retrieval operations on the same conceptual combinations.