---
abstract: 'In a recent article \[Phys. Rev. A [**54**]{}, 1793 (1996)\] Krenn and Zeilinger investigated the conditional two-particle correlations for the subensemble of data obtained by selecting the results of the spin measurements by two observers 1 and 2 with respect to the result found in the corresponding measurement by a third observer. In this paper we write out explicitly the condition required in order for the selected results of observers 1 and 2 to violate Bell’s inequality for general measurement directions $\vec{e}_1$, $\vec{e}\, ^{\prime}_{1}$, $\vec{e}_2$, $\vec{e}\,^{\prime}_{2}$, and $\vec{e}_3$. It is shown that there are infinitely many sets of directions giving the maximum level of violation. Further, we extend the analysis by the authors to the class of triorthogonal states $|\Psi \rangle = c_1 |z_1 \rangle |z_2 \rangle |z_3 \rangle + c_2 |-z_1 \rangle |-z_2 \rangle |-z_3 \rangle$. It is found that a maximal violation of Bell’s inequality occurs provided the corresponding three-particle state yiels a direct (“all or nothing”) nonlocality contradiction.'
address: 'C/Alto del León 8, 4A, 28038 Madrid, Spain'
author:
- 'José L. Cereceda'
date: 27 May 1999
title: '[Two-particle entanglement as a property of three-particle entangled states]{}[^1]'
---

[2]{}

Introduction
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Recently, Krenn and Zeilinger [@KZ] 