Cabello's nonlocality for generalized three-qubit GHZ states

TL;DR

This paper investigates Cabello's nonlocality argument for three-qubit generalized GHZ states, showing it applies to almost all entangled states with a maximum success probability of about 14%, slightly higher than Hardy's argument.

Contribution

It demonstrates the applicability of Cabello's nonlocality argument to generalized three-qubit GHZ states and compares its success probability with Hardy's argument under different theories.

Findings

CNA applies to almost all entangled three-qubit GHZ states.

Maximum success probability of CNA is approximately 14%.

Success probabilities can reach 50% in generalized no-signaling theories.

Abstract

In this note, we study Cabello's nonlocality argument (CNA) for three-qubit systems configured in the generalized GHZ state. For this class of states, we show that CNA runs for almost all entangled ones, and that the maximum probability of success of CNA is 14% (approx.), which is attained for the maximally entangled GHZ state. This maximum probability is slightly higher than that achieved for the standard Hardy's nonlocality argument (HNA) for three qubits, namely 12.5%. Also, we show that the success probability of both HNA and CNA for three-qubit systems can reach a maximum of 50% in the framework of generalized no-signaling theory.