Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation
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.
Keywords
Cite
@article{arxiv.2011.02657,
title = {Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation},
author = {Peter Millington and Zong-Gang Mou and Paul M. Saffin and Anders Tranberg},
journal= {arXiv preprint arXiv:2011.02657},
year = {2021}
}
Comments
21 pages, 1 figure; more references added; minor corrections in line with published version, the order of references does not match the published version