### Bell inequalities and distillability in N-quantum-bit systems

**Antonio Acin, Valerio Scarani, Michael M. Wolf**

Phys. Rev. A 66, 042323 **, (2002)

**DOI**: 10.1103/PhysRevA.66.042323

^{}

*arXiv.org*: quant-ph/0206084

^{}

**Abstract:**The relation between Bell inequalities with two two-outcome measurements per site and distillability is analyzed in systems of an arbitrary number of quantum bits. We observe that the violation of any of these inequalities by a quantum state implies that pure-state entanglement can be distilled from it. The corresponding distillation protocol may require that some of the parties join into several groups. We show that there exists a link between the amount of the Bell inequality violation and the size of the groups they have to form for distillation. Thus, a strong violation is always sufficient for full N-partite distillability. This result also allows for a security proof of multi-partite quantum key distribution (QKD) protocols.