Quantum Nonlocality Enhanced by Homogenization

TL;DR

This paper investigates how homogenization affects quantum nonlocality in Bell inequalities, showing it can enhance violations for some inequalities and alter the quantum violation domains for generalized GHZ states.

Contribution

It analyzes the effects of homogenization on Hardy and tight Bell inequalities, revealing increased violations and domain changes in quantum nonlocality.

Findings

Homogenization strengthens quantum violation in Hardy inequalities.

Homogenization causes violations in inequalities previously without quantum violation.

Quantum violation domains for homogenized Hardy inequalities are smaller for generalized GHZ states.

Abstract

Homogenization proposed in [Y.-C Wu and M. \.Zukowski, Phys. Rev. A 85, 022119 (2012)] is a procedure to transform a tight Bell inequality with partial correlations into a full-correlation form that is also tight. In this paper, we check the homogenizations of two families of $n$-partite Bell inequalities: the Hardy inequality and the tight Bell inequality without quantum violation. For Hardy's inequalities, their homogenizations bear stronger quantum violation for the maximally entangled state; the tight Bell inequalities without quantum violation give the boundary of quantum and supra-quantum, but their homogenizations do not have the similar properties. We find their homogenization are violated by the maximally entangled state. Numerically computation shows the the domains of quantum violation of homogenized Hardy's inequalities for the generalized GHZ states are smaller than those of Hardy's inequalities.