Optimal GHZ Paradox for Three Qubits

TL;DR

This paper identifies an optimal GHZ paradox state that maximally demonstrates quantum nonlocality for a given purity level, revealing how mixed states can still exhibit strong nonlocal correlations.

Contribution

It introduces a novel method to find the optimal state saturating the nonlocality-purity tradeoff, showing that a GHZ state with flipped color noise achieves maximal nonlocality resistance.

Findings

Optimal state can violate the logical inequality maximally at fixed purity.

The optimal state is a GHZ state with flipped color noise.

Maximum noise resistance of 50% for the optimal state.

Abstract

Quatum nonlocality as a valuable resource is of vital importance in quantum information processing. The characterization of the resource has been extensively investigated mainly for pure states, while relatively less is know for mixed states. Here we prove the existence of the optimal GHZ paradox by using a novel and simple method to extract an optimal state that can saturate the tradeoff relation between quantum nonlocality and the state purity. In this paradox, the logical inequality which is formulated by the GHZ-typed event probabilities can be violated maximally by the optimal state for any fixed amount of purity (or mixedness). Moreover, the optimal state can be described as a standard GHZ state suffering flipped color noise. The maximal amount of noise that the optimal state can resist is 50%. We suggest our result to be a step toward deeper understanding of the role played by the AVN proof of quantum nonlocality as a useful physical resource.