Bipartite polygon models: entanglement classes and their nonlocal behaviour

TL;DR

This paper explores Hardy's nonlocality in bipartite polygon models, revealing how entangled states exhibit nonlocal behavior and uncovering a connection to almost-quantum correlations within a broad operational framework.

Contribution

It introduces a systematic method to classify entangled states in polygon models and links their nonlocal behavior to geometric and symmetry properties, extending understanding beyond qubit systems.

Findings

Odd polygon models show similar Hardy nonlocality to qubits.

Mixed-state Hardy nonlocality depends on symmetry in dynamics.

Identification of an almost-quantum correlation class.

Abstract

Hardy's argument constitutes an elegantly logical test for identifying nonlocal features of multipartite correlations. In this paper, we investigate Hardy's nonlocal behavior within a broad class of operational theories, including the qubit state space as a specific case. Specifically, we begin by examining a wider range of operational models with state space descriptions in the form of regular polygons. First, we present a systematic method to characterize the possible forms of entangled states within bipartite compositions of these models. Then, through explicit examples, we identify the classes of entangled states that exhibit Hardy-type nonlocality. Remarkably, our findings highlight a closer analogy between odd polygon models and the qubit state space in terms of their bipartite Hardy nonlocal behavior compared to even-sided polygons. Furthermore, we demonstrate that the emergence of mixed-state Hardy nonlocality in any operational model is determined by a specific symmetry inherent in its dynamic description. Finally, our results uncover an unexplored class of almost-quantum correlations that can be associated with an explicit operational model.