Non-locality in high spin systems with tensor correlations

TL;DR

This paper investigates how non-locality can be detected in high-spin systems using tensor correlations, revealing that standard Bell inequalities can identify non-locality across different spin magnitudes, but detection becomes challenging when correlations are limited.

Contribution

It introduces a framework for detecting non-locality in high-spin systems via tensor correlations and characterizes observables that genuinely reflect non-locality beyond standard measurement setups.

Findings

Non-locality detectable via Bell inequality violations for all N.

Detection efficacy depends on the order of correlations and spin magnitude.

Standard measurement setups may not suffice to reveal non-locality in higher dimensions.

Abstract

We address the problem of detecting non-locality in coupled N level systems in the language of spin. Through a number of examples, we show that non-locality can be detected via a violation of the standard Bell inequality, irrespective of what N is, with correlations from observables of order k ~ 2s in the fundamental spin operators. We further show that, contrarily, if the order k is frozen, then non-locality eludes a detection when s >> k, leading to a weak classical limit. Armed with these results, we proceed to characterize observables that 'genuinely' reflect non-locality in higher dimensions, and demonstrate that one needs to go beyond the standard set-ups such as Stern-Gerlach and those with correlations involving measurement of spin projections along quantization axes.