A classification of multipartite states by degree of non-locality

TL;DR

This paper introduces a new classification of multipartite quantum states based on their maximum non-locality, using a hierarchy of contextuality notions, and provides evidence that most entangled states are logically non-local.

Contribution

It proposes a novel classification framework for multipartite states based on non-locality levels and supports the conjecture that all entangled states beyond two parties are logically contextual.

Findings

All permutation-symmetric states are logically non-local.

Balanced states with Boolean function structures are also logically non-local.

Supports the conjecture that all multi-party entangled states are logically contextual.

Abstract

We propose a novel form of classification of multipartite states, in terms of the maximum degree of non-locality they can exhibit under any choice of local observables. This uses the hierarchy of notions previously introduced by Abramsky and Brandenburger: strong contextuality, logical contextuality, and probabilistic contextuality. We study n-qubit pure states. We conjecture that for more than 2 parties, all entangled states are logically contextual. We prove a number of results in support of this conjecture: (1) We show that all permutation-symmetric states are logically non-local. (2) We study the class of balanced states with functional dependencies. These states are described by Boolean functions and have a rich structure, allowing a detailed analysis, which again confirms the conjecture in this case.