Multipartite Bell-type Inequality by Generalizing Wigner's Argument

TL;DR

This paper generalizes Wigner's Bell-type inequality for any N-partite quantum state, demonstrating its violation by quantum mechanics and comparing its robustness against noise with other multipartite inequalities.

Contribution

It introduces a generalized Wigner's inequality applicable to any N-partite state and analyzes its violation and robustness compared to existing inequalities.

Findings

GWI is violated by all pure entangled states.

GWI's robustness is quantified via threshold visibilities for various states.

Comparison shows GWI's effectiveness in detecting entanglement under noise.

Abstract

Wigner's argument inferring Bell-type inequality for the EPR-Bohm entangled state is generalized here for any N-partite state. This is based on assuming for the relevant dichotomic observables the existence of the overall joint probability distributions, satisfying the locality condition, that would yield the measurable marginal probabilities. For any N, such Generalized Wigner's Inequality (GWI) is violated by quantum mechanics for all pure entangled states. The efficacy of GWI is probed, comparing with the Seevinck-Svetlichny multipartite Bell-type inequality, by calculating threshold visibilities for the quadripartite GHZ, Cluster andWstates that determine their respective robustness with respect to the quantum mechanical violation of GWI in the presence of white noise.