A framework for the study of symmetric full-correlation Bell-like inequalities

TL;DR

This paper introduces a comprehensive framework for symmetric full-correlation Bell-like inequalities, enabling the derivation of new inequalities and tools for analyzing quantum correlations in multipartite systems.

Contribution

It provides a novel framework for symmetric full-correlation Bell-like inequalities, leading to new Svetlichny, entanglement, and Tsirelson inequalities for multipartite quantum systems.

Findings

Derived new Svetlichny inequalities for arbitrary parties, settings, and outcomes.

Developed two-outcome device-independent entanglement witnesses for genuine n-partite entanglement.

Formulated two-outcome Tsirelson inequalities applicable to various multipartite scenarios.

Abstract

Full-correlation Bell-like inequalities represent an important subclass of Bell-like inequalities that have found applications in both a better understanding of fundamental physics and in quantum information science. Loosely speaking, these are inequalities where only measurement statistics involving all parties play a role. In this paper, we provide a framework for the study of a large family of such inequalities that are symmetrical with respect to arbitrary permutations of the parties. As an illustration of the power of our framework, we derive (i) a new family of Svetlichny inequalities for arbitrary numbers of parties, settings and outcomes, (ii) a new family of two-outcome device-independent entanglement witnesses for genuine n-partite entanglement and (iii) a new family of two-outcome Tsirelson inequalities for arbitrary numbers of parties and settings. We also discuss briefly the application of these new inequalities in the characterization of quantum correlations.