Entanglement and maximal violation of the CHSH inequality in a system of two spins j: a novel construction and further observations

TL;DR

This paper investigates entanglement and CHSH inequality violations in a two-spin system of arbitrary spin $j$, introducing a new operator construction that confirms maximal violation consistent with Tsirelson's bound.

Contribution

A novel construction of the CHSH operator for two-spin $j$ systems and analysis of its violation in the singlet state, extending understanding of quantum correlations.

Findings

Maximal CHSH violation observed in the singlet state.

Construction aligns with previous methods despite differences.

Violations reach Tsirelson's bound for arbitrary spin $j$.

Abstract

We study the CHSH inequality for a system of two spin $j$ particles, for generic $j$. The CHSH operator is constructed using a set of unitary, Hermitian operators $\left\{ A_{1},A_{2},B_{1},B_{2}\right\} $. The expectation value of the CHSH operator is analyzed for the singlet state $\left|\psi_{s}\right\rangle $. Being $\left|\psi_{s}\right\rangle $ an entangled state, a violation of the CHSH inequality compatible with Tsirelson's bound is found. Although the construction employed here differs from that of [1], full agreement is recovered.