Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes

TL;DR

This paper investigates the limits of nonlocal correlations when signaling is allowed, showing that Tsirelson bounds still hold under certain conditions and connecting these findings to topological zero modes.

Contribution

It extends the understanding of nonlocal correlations beyond non-signaling theories, demonstrating the persistence of Tsirelson bounds with signaling and linking to parafermionic zero modes.

Findings

Tsirelson bounds remain valid with signaling if Hilbert space structure is preserved

Novel relations between non-locality, local correlations, and signaling are identified

Parafermionic zero modes can simulate signaling theories and exhibit distinct correlation behaviors

Abstract

Bell's theorem renders quantum correlations distinct from those of any local-realistic model. Although being stronger than classical correlations, quantum correlations are limited by the Tsirelson bound. This bound, however, applies for Hermitian, commutative operators corresponding to non-signaling observables in Alice's and Bob's spacelike-separated labs. As an attempt to explore theories beyond quantum mechanics and analyze the uniqueness of the latter, we examine in this work the extent of non-local correlations when relaxing these fundamental assumptions, which allows for theories with non-local signaling. We prove that, somewhat surprisingly, the Tsirelson bound in the Bell-Clauser-Horne-Shimony-Holt scenario, and similarly other related bounds on non-local correlations, remain effective as long as we maintain the Hilbert space structure of the theory. Furthermore, in the case of Hermitian observables we find novel relations between non-locality, local correlations, and signaling. We demonstrate that such non-local signaling theories are naturally simulated by quantum systems of parafermionic zero modes. We numerically study the derived bounds in parafermionic systems, confirming the bounds' validity yet finding a drastic difference between correlations of 'signaling' and 'non-signaling' sets of observables. We also propose an experimental procedure for measuring the relevant correlations.