On the violation of Bell's inequality for all non-product quantum states

TL;DR

This paper revisits Gisin's 1991 proof demonstrating that all pure entangled two-particle states violate Bell's inequality, clarifying mathematical details to reinforce the original physical conclusions.

Contribution

It provides a clearer, pedagogical reexamination of Gisin's proof, strengthening understanding of Bell inequality violations for all pure entangled states.

Findings

All pure entangled states violate Bell's inequality

Clarified mathematical steps in Gisin's original proof

Reinforced the universality of Bell inequality violation for pure entangled states

Abstract

We present an explicit reexamination of Gisin's 1991 original proof concerning the violation of Bell's inequality for any pure entangled state of two-particle systems. Given the relevance of Gisin's work, our analysis is motivated by pedagogical reasons and allows the straightening of a few mathematical points in the original proof that in no way change the physical conclusions reached by Gisin.