Crypto-nonlocality in arbitrarily dimensional systems

TL;DR

This paper extends the crypto-nonlocality model to higher dimensions and develops Leggett-type inequalities for arbitrary dimensions, enhancing understanding of quantum correlations beyond quantum mechanics.

Contribution

It generalizes the crypto-nonlocality framework to any dimension and creates testable inequalities, advancing the study of nonlocal models in quantum physics.

Findings

Extended crypto-nonlocal model to higher dimensions

Developed Leggett-type inequalities for arbitrary dimensions

Identified models with predictions exceeding quantum mechanics

Abstract

According to Bell's theorem, any model based on local variables cannot reproduce certain quantum correlations. A critical question is whether one could devise an alternative framework, based on nonlocal variables, to reproduce quantum correlations while adhering to fundamental principles. Leggett proposed a nonlocal model, termed crypto-nonlocality, rooted in considerations of the reality of photon polarization, but this property restricted it to being bi-dimensional. In this Letter, we extend the crypto-nonlocal model to higher dimensions and develop a framework for constructing experimentally testable Leggett-type inequalities for arbitrary dimensions. Our investigation into models that yield specific predictions exceeding those of quantum mechanics is intriguing from an information-theoretic perspective and is expected to deepen our understanding of quantum correlations.