Multipartite Bell-type Inequality by Generalizing Wigner's Argument

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.

References in corpus (5)

• The maximally entangled symmetric state in terms of the geometric measure
• All entangled pure states violate a single Bell's inequality
• Maximally entangled three-qubit states via geometric measure of entanglement
• Bell's theorem as a signature of nonlocality: a classical counterexample
• Classical statistical distributions can violate Bell-type inequalities

Cited by in corpus (15)

• Universal Limitations on Quantum Key Distribution over a Network
• Generalized Hardy's Paradox
• Speed limits on correlations in bipartite quantum systems
• Increased success probability in Hardy's nonlocality: Theory and demonstration
• Inequivalent Leggett-Garg inequalities
• Quantum mechanical violation of macrorealism for large spin and its robustness against coarse-grained measurements
• Fundamental limitations on the device-independent quantum conference key agreement
• Bipartite qutrit local realist inequalities and the robustness of their quantum mechanical violation
• Persistence of quantum violation of macrorealism for large spins even under coarsening of measurement times
• Violation of generalized Bell inequality and its optimal measurement settings
• Testing of quantum nonlocal correlations under constrained free will and imperfect detectors
• Experimental construction of a symmetric three-qubit entangled state and its utility in testing the violation of a Bell inequality on an NMR quantum simulator
• Maximum violation of Wigner inequality for two-spin entangled states with parallel and antiparallel polarizations
• Extended Bell inequality and maximum violation
• Wigner's approach enabled detection of multipartite nonlocality using all different bipartitions