The relation between nonlocality and contextuality for a biphoton

TL;DR

This paper explores the relationship between nonlocality and contextuality in biphoton systems, showing that all KCBS-contextual states are nonlocal under CHSH, but not vice versa, revealing nuanced quantum correlations.

Contribution

It establishes a connection between contextuality and nonlocality in biphoton states, highlighting that KCBS-contextual states are always CHSH-nonlocal, unlike the reverse.

Findings

KCBS-contextual biphoton states are CHSH-nonlocal

Not all CHSH-nonlocal states are KCBS-contextual

Provides insight into quantum correlations in biphoton systems

Abstract

We investigate the set of qutrit states in terms of symmetric states of two qubits that violate the minimal contextual inequality, namely the Klyachko-Can-Binicoglu-Shumovsky (KCBS) inequality. The physical system that provides a natural framework for this problem is a biphoton which consists of two photons in the same spatio-temporal mode and whose effective polarization behaves as a three-level quantum system. The relationship between the KCBS contextual inequality and the Clauser-Horne-Shimony-Holt (CHSH) inequality is investigated. We find that every biphotonic state that is contextual with respect to KCBS is nonlocal as per the CHSH test when the two photons are apart, but the converse is not true.