Here we show that spin-lattices can serve as a test object for quantum foundations and quantum information theory, revealing unsuspected properties. We propose a (thought) experiment on such lattices that mimics the Bell- experiment and calculate the outcomes and the Bell inequality. It appears that for a wide range of geometries the Bell- inequality is violated, even if these lattices are local according to the usual definitions. Some spin-1/2 lattices can even violate the Bell inequality more than the Tsirelson bound. We argue that there is no consensual explanation for this result. We make the link with problems in quantum foundations and quantum information theory.
The purpose of the conference (the fourth in the series of Vaxjo conferences) was to bring together scientists (physicists, mathematicians and philosophers) who are interested in foundations of quantum physics. An emphasis was made on both theory and experiment, the underlying objective being to offer to the physical, mathematical and philosophic communities a truly interdisciplinary conference as a privileged place for a scientific interaction. Due to the actual increased role of foundations in the development of quantum information theory as well as the necessity to reconsider foundations at the beginning of the new millennium, the organizers of the conference decided that it was just the right time for taking the scientific risk of trying this.