Inflated Graph States Refuting Communication-Assisted LHV Models

TL;DR

This paper introduces inflated graph states that demonstrate correlations incompatible with any communication-assisted local hidden variable models, extending previous Bell inequality violations to more complex quantum network states.

Contribution

It systematically extends graph states into inflated versions that refute communication-assisted LHV models, including the smallest known examples with 4, 5, and 7 qubits.

Findings

Smallest 4-qubit violation with binary inputs and outputs

7-qubit linear graph state as the minimal example

Systematic method to inflate any graph state for nonlocal correlations

Abstract

Standard Bell inequalities hold when distant parties are not allowed to communicate. Barrett et al. found correlations from Pauli measurements on certain network graphs refute a local hidden variable (LHV) description even allowing some communication along the graph. This has recently found applications in proving separation between classical and quantum computing, in terms of shallow circuits, and distributed computing. The correlations presented by Barrett et al. can be understood as coming from an extension of three party GHZ state correlations which can be embedded on a graph state. In this work, we propose systematic extensions of any graph state, which we dub inflated graph states such that they exhibit correlations which refute any communication assisted LHV model. We further show the smallest possible such example, with a 7-qubit linear graph state, as well as specially crafted smaller examples with 5 and 4 qubits. The latter is the smallest possible violation using binary inputs and outputs.