Direct evaluation of pure graph state entanglement

Abstract

We address the question of quantifying entanglement in pure graph states. Evaluation of multipartite entanglement measures is extremely hard for most pure quantum states. In this paper we demonstrate how solving one problem in graph theory, namely the identification of maximum independent set, allows us to evaluate three multipartite entanglement measures for pure graph states. We construct the minimal linear decomposition into product states for a large group of pure graph states, allowing us to evaluate the Schmidt measure. Furthermore we show that computation of distance-like measures such as relative entropy of entanglement and geometric measure becomes tractable for these states by explicit construction of closest separable and closest product states respectively. We show how these separable states can be described using stabiliser formalism as well as PEPs-like construction. Finally we discuss the way in which introducing noise to the system can optimally destroy entanglement.

arXiv comment23 pages, 9 figures

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• Symmetric hypergraph states: Entanglement quantification and robust Bell nonlocality
• Group structures and representations of graph states
• Finding maximal quantum resources
• The Foliage Partition: An Easy-to-Compute LC-Invariant for Graph States
• Distinguishing Graph States by the Properties of Their Marginals