Quantum-Mechanical Correlations and Tsirelson Bound from Geometric Algebra

• URL: http://arxiv.org/abs/2007.05301v3
• Date: Thu, 12 Nov 2020 10:08:58 GMT
• Title: Quantum-Mechanical Correlations and Tsirelson Bound from Geometric Algebra
• Authors: Carsten Held
• Abstract summary: We 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. All correlations, QM and classical, respect a QM bound (the Tsirelson bound)
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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