Entanglement Witnesses for Graph States: General Theory and Examples

TL;DR

This paper develops a comprehensive framework for constructing entanglement witnesses tailored for graph states, improving detection capabilities and noise tolerance, with explicit examples and analytical methods for general cases.

Contribution

Introduces a general theory for entanglement witnesses in graph states, providing explicit examples and analytical constructions with high noise tolerance.

Findings

Explicit witnesses for all graph states up to six qubits

Witnesses with noise tolerance approaching one as particle number increases

Enhanced detection of genuine multipartite entanglement

Abstract

We present a general theory for the construction of witnesses that detect genuine multipartite entanglement in graph states. First, we present explicit witnesses for all graph states of up to six qubits which are better than all criteria so far. Therefore, lower fidelities are required in experiments that aim at the preparation of graph states. Building on these results, we develop analytical methods to construct two different types of entanglement witnesses for general graph states. For many classes of states, these operators exhibit white noise tolerances that converge to one when increasing the number of particles. We illustrate our approach for states such as the linear and the 2D cluster state. Finally, we study an entanglement monotone motivated by our approach for graph states.