Three-outcome multipartite Bell inequalities: applications to dimension witnessing and spin-nematic squeezing in many-body systems

TL;DR

This paper introduces a three-outcome Bell inequality tailored for many-body spin-1 systems, enabling experimental detection of nonlocal correlations and dimension witnessing in complex quantum states like spin-nematic squeezed states.

Contribution

It develops a new Bell inequality for spin-1 systems and scalable witnesses for dimension certification, advancing nonlocality detection in many-body quantum systems.

Findings

Derived practical Bell correlation witnesses for collective spin measurements.

Established scalable Bell dimension witnesses for certifying three-level correlations.

Applied witnesses to spin-nematic squeezed states in Bose-Einstein condensates.

Abstract

We present a three-outcome permutationally-invariant Bell inequality, which we show to be naturally suited to explore nonlocal correlations in many-body spin-1 systems or SU(3) models. In the specific, we show how to derive from this inequality experimentally practical Bell correlation witnesses based on the measurement of collective spin components. Moreover, we present approaches that allow us to derive scalable Bell dimension witnesses, namely criteria whose violation signals the impossibility of reproducing the observed statistics by single-particle Hilbert spaces of a certain dimension.This enables the certification of genuine three-level correlations that cannot occur in two-level, i.e. qubit, systems. As an example, we show the application of these witnesses in spin-nematic squeezed states, such as the one that can be prepared in spin-1 Bose-Einstein condensates.