True Multipartite Entanglement Hardy Test

TL;DR

This paper introduces a new Hardy test for multipartite entanglement that identifies genuine entanglement through specific conditions rather than inequalities, demonstrating its effectiveness for pure states.

Contribution

It extends Hardy's paradox to multipartite systems, providing a novel criterion for detecting true multipartite entanglement using marginal probabilities.

Findings

The Hardy-based test can only be satisfied by genuinely multipartite entangled states.

The resolving state for the paradox is unique and pure for qubit systems.

The method does not rely on statistical inequalities, offering a different approach to entanglement detection.

Abstract

Quantum mechanics allows systems to be entangled with each other, which results in stronger than classical correlations. Many methods of identifying entanglement have been proposed over years, most of which are based on violating some statistical inequalities. In this work we extend the idea due to Hardy, in which entanglement is not identified with use of statistical inequalities, but by simultaneous satisfaction of certain conditions. We show that the new variant of the Hardy paradox relying on marginal probabilities can be resolved only by true multipartite entangled states. Also, the state resolving this paradox for given local measurements is pure and unique in case of qubit collections.