Multipartite positive-partial-transpose inequalities exponentially stronger than local reality inequalities

TL;DR

This paper introduces new Bell correlation inequalities derived from the positivity of all partial transposes of N-partite quantum states, which are exponentially stronger than standard inequalities and can detect certain bound entangled states.

Contribution

It establishes a novel set of inequalities based on partial transpose positivity that surpass traditional Bell inequalities in strength and can identify bound entangled states.

Findings

Inequalities are exponentially stronger than standard Bell inequalities.

Violations indicate the presence of bipartite distillable entanglement.

Certain bound entangled states violate these inequalities for N≥4.

Abstract

We show that positivity of {\it every} partial transpose of $N$-partite quantum states implies new inequalities on Bell correlations which are stronger than standard Bell inequalities by a factor of $2^{(N-1)/2}$. A violation of the inequality implies the system is in a bipartite distillable entangled state. It turns out that a family of $N$-qubit bound entangled states proposed by D\"ur {[Phys. Rev. Lett. {\bf 87}, 230402 (2001)]} violates the inequality for $N\geq 4$.