Multiparticle entanglement in graph-diagonal states: Necessary and sufficient conditions for four qubits

TL;DR

This paper provides a complete characterization of genuine multiparticle entanglement for specific four- and five-qubit graph states, including noisy states, advancing understanding in quantum entanglement theory.

Contribution

It offers necessary and sufficient conditions for multiparticle entanglement in four-qubit graph-diagonal states and extends to certain five-qubit states with noise.

Findings

Complete characterization for four-qubit cluster-state basis

Entanglement criteria for five-qubit Y-shaped graph states with noise

Extension to a family of graph states with arbitrary qubits

Abstract

The characterization of genuine multiparticle entanglement is important for entanglement theory as well as experimental studies related to quantum information theory. Here, we completely characterize genuine multiparticle entanglement for four-qubit states diagonal in the cluster-state basis. In addition, we give a complete characterization of multiparticle entanglement for all five-qubit graph states mixed with white noise, for states diagonal in the basis corresponding to the five-qubit Y-shaped graph, and for a family of graph states with an arbitrary number of qubits.