A Classification Program for Nonlocality Paradoxes of Three Qubits

TL;DR

This paper develops a classification program for nonlocality paradoxes in three-qubit systems, introducing new families and aiming for a complete taxonomy of such paradoxes.

Contribution

It introduces new infinite families of three-qubit nonlocality paradoxes and provides a roadmap towards their complete classification.

Findings

Exhaustive classification of three-qubit paradoxes under regularity conditions

Identification of a highly exotic paradox example

Constraints and conjectures on the nature of all such paradoxes

Abstract

Nonlocality is a quintessential signature of nonclassical behaviour and a resource for quantum advantages in communication and computation. The paradoxical correlations witnessed by strong nonlocality undergird the standard probabilistic form of nonlocality and provide optimal advantages in numerous informational tasks. Three-qubit systems are the simplest ones that admit strong nonlocality. Abramsky et al. (TQC, 2017) established the existence of an infinite family of three-qubit paradoxes, beyond the well-known GHZ paradox, which exhibited a novel conditional structure. In this work, we introduce several new infinite families of three-qubit paradoxes and articulate a detailed roadmap towards the complete classification of all three-qubit nonlocality paradoxes. In particular, we prove that our paradoxes exhaust all those satisfying reasonable regularity conditions. We give an example of a highly exotic paradox and place constraints on the search for new exotic paradoxes. We conjecture that all paradoxes must involve states from a one-parameter family and provide significant evidence in support of this conjecture.