N-particle nonclassicality without N-particle correlations

TL;DR

This paper introduces new Bell inequalities that detect genuine N-partite entanglement using only (N-1)-partite correlations, revealing entanglement in states lacking full N-partite correlations, with potential quantum information applications.

Contribution

It develops a method to derive Bell inequalities involving fewer correlations that can still detect genuine N-partite entanglement, including non-linear forms.

Findings

Inequalities detect five-partite entanglement with only four-partite correlations.

States can violate these inequalities without having N-partite correlations.

Potential applications in quantum information tasks.

Abstract

Most of known multipartite Bell inequalities involve correlation functions for all subsystems. They are useless for entangled states without such correlations. We give a method of derivation of families of Bell inequalities for N parties, which involve, e.g., only (N-1)-partite correlations, but still are able to detect proper N-partite entanglement. We present an inequality which reveals five-partite entanglement despite only four-partite correlations. Classes of inequalities introduced here can be put into a handy form of a single non-linear inequality. An example is given of an N qubit state, which strongly violates such an inequality, despite having no N-qubit correlations. This surprising property might be of potential value for quantum information tasks.