Quantum-Mechanical Correlations and Tsirelson Bound from Geometric Algebra
arXiv:2007.05301 · doi:10.1007/s40509-021-00252-y
Abstract
The Bell-Clauser-Horne-Shimony-Holt inequality can be used to show that no local hidden-variable theory can reproduce the correlations predicted by quantum mechanics (QM). It can be proved that certain QM correlations lead to a violation of the classical bound established by the inequality, while all correlations, QM and classical, respect a QM bound (the Tsirelson bound). Here, we show that these well-known results depend crucially on the assumption that the values of physical magnitudes are scalars. The result implies, first, that the origin of the Tsirelson bound is geometrical, not physical; and, second, that a local hidden-variable theory does not contradict QM if the values of physical magnitudes are vectors.
Revised key argument, removed superfluous reference to anticorrelations