Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation

• URL: http://arxiv.org/abs/2011.02657v3
• Date: Thu, 1 Apr 2021 04:21:12 GMT
• Title: Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation
• Authors: Peter Millington, Zong-Gang Mou, Paul M. Saffin, Anders Tranberg
• Abstract summary: We consider the Classical-Statistical approximation in the context of Bell-type inequalities. We show that the approximation does not violate temporal Bell-type inequalities, even though it is in some sense exact for a free theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Inspired by Lefschetz thimble theory, we treat Quantum Field Theory as a statistical theory with a complex Probability Distribution Function (PDF). Such complex-valued PDFs permit the violation of Bell-type inequalities, which cannot be violated by a real-valued, non-negative PDF. In this paper, we consider the Classical-Statistical approximation in the context of Bell-type inequalities, viz. the familiar (spatial) Bell inequalities and the temporal Leggett-Garg inequalities. We show that the Classical-Statistical approximation does not violate temporal Bell-type inequalities, even though it is in some sense exact for a free theory, whereas the full quantum theory does. We explain the origin of this discrepancy, and point out the key difference between the spatial and temporal Bell-type inequalities. We comment on the import of this work for applications of the Classical-Statistical approximation.

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