Witnessing Bell violations through probabilistic negativity

Morris, Benjamin; Fiderer, Lukas J.; Lang, Ben; Goldwater, Daniel

Abstract

Bell's theorem shows that no local hidden-variable model can explain the measurement statistics of a quantum system shared between two parties, thus ruling out a classical (local) understanding of nature. In this paper we demonstrate that by relaxing the positivity restriction in the hidden-variable probability distribution it is possible to derive quasiprobabilistic Bell inequalities whose sharp upper bound is written in terms of a negativity witness of said distribution. This provides an analytic solution for the amount of negativity necessary to violate the Clauser-Horne-Shimony-Holt inequality by an arbitrary amount, therefore revealing the amount of negativity required to emulate the quantum statistics in a Bell test.

• Journal Article Type: Article
• Acceptance Date: Feb 8, 2022
• Online Publication Date: Mar 2, 2022
• Publication Date: Mar 2, 2022
• Deposit Date: Mar 4, 2022
• Publicly Available Date: Mar 4, 2022
• Journal: Physical Review A
• Print ISSN: 2469-9926
• Electronic ISSN: 2469-9934
• Publisher: American Physical Society (APS)
• Peer Reviewed: Peer Reviewed
• Volume: 105
• Issue: 3
• Article Number: 032202
• DOI: https://doi.org/10.1103/physreva.105.032202
• Public URL: https://nottingham-repository.worktribe.com/output/7536211
• Publisher URL: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.032202