Multipartite bound entanglement and multi-setting Bell inequalities

TL;DR

This paper demonstrates that for sufficiently many measurement settings, there exist multipartite bound entangled states that violate Bell inequalities starting from four qubits, expanding understanding of quantum nonlocality.

Contribution

It introduces new Bell inequalities with multiple settings and proves bound entangled states violate them for N≥4, improving previous bounds.

Findings

Bound entangled states violate multi-setting Bell inequalities for N≥4

Violation occurs with sufficiently large number of measurement settings

Results extend the understanding of quantum nonlocality in multipartite systems

Abstract

D\"{u}r [Phys. Rev. Lett. {\bf 87}, 230402 (2001)] constructed $N$-qubit bound entangled states which violate a Bell inequality for $N\ge 8$, and his result was recently improved by showing that there exists an $N$-qubit bound entangled state violating the Bell inequality if and only if $N\ge 6$ [Phys. Rev. A {\bf 79}, 032309 (2009)]. On the other hand, it has been also shown that the states which D\"{u}r considered violate Bell inequalities different from the inequality for $N\ge 6$. In this paper, by employing different forms of Bell inequalities, in particular, a specific form of Bell inequalities with $M$ settings of the measuring apparatus for sufficiently large $M$, we prove that there exists an $N$-qubit bound entangled state violating the $M$-setting Bell inequality if and only if $N\ge 4$.