Complete proof of Gisin's theorem for three qubits

TL;DR

This paper proves that all pure three-qubit entangled states violate a Bell-type inequality, extending Gisin's theorem from bipartite to tripartite systems using Hardy’s non-locality argument.

Contribution

It provides the first complete proof that all three-qubit pure entangled states violate a Bell-type inequality, confirming a Gisin-type theorem for three qubits.

Findings

All three-qubit pure entangled states violate a Bell-type inequality.

The proof is analytical and based on Hardy's non-locality argument.

This extends Gisin's theorem to three-qubit systems.

Abstract

Gisin's theorem assures that for any pure bipartite entangled state, there is violation of Bell-CHSH inequality revealing its contradiction with local realistic model. Whether, similar result holds for three-qubit pure entangled states, remained unresolved. We show analytically that all three-qubit pure entangled states violate a Bell-type inequality, derived on the basis of local realism, by exploiting the Hardy's non-locality argument.