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We present the results of two tests where a sample of human participants wereasked to make judgements about the conceptual combinations {\it The AnimalActs} and {\it The Animal eats the Food}. Both tests significantly violate theClauser-Horne-Shimony-Holt version of Bell inequalities (`CHSH inequality'),thus exhibiting manifestly non-classical behaviour due to the meaningconnection between the individual concepts that are combined. We then apply aquantum-theoretic framework which we developed for any Bell-type situation andrepresent empirical data in complex Hilbert space. We show that the observedviolations of the CHSH inequality can be explained as a consequence of a strongform of `quantum entanglement' between the component conceptual entities inwhich both the state and measurements are entangled. We finally observe that aquantum model in Hilbert space can be elaborated in these Bell-type situationseven when the CHSH violation exceeds the known `Cirel'son bound', in contrastto a widespread belief. These findings confirm and strengthen the results werecently obtained in a variety of cognitive tests and document and imageretrieval operations on the same conceptual combinations.

Entanglement in Cognition violating Bell Inequalities Beyond Cirel'son's Bound