Entanglement and local information access for graph states

Abstract

We exactly evaluate a number of multipartite entanglement measures for a class of graph states, including d-dimensional cluster states (d = 1,2,3), the Greenberger-Horne-Zeilinger states, and some related mixed states. The entanglement measures that we consider are continuous, `distance from separable states' measures, including the relative entropy, the so-called geometric measure, and robustness of entanglement. We also show that for our class of graph states these entanglement values give an operational interpretation as the maximal number of graph states distinguishable by local operations and classical communication (LOCC), as well as supplying a tight bound on the fixed letter classical capacity under LOCC decoding.

8 pages, 4 figures, to appear in the special issue of New J. Phys. on measurement-based quantum information processing

References in corpus (9)

• Multi-party entanglement in graph states
• Experimental entanglement of six photons in graph states
• Universal resources for measurement-based quantum computation
• Entanglement purification protocols for all graph states
• Ground state approximation for strongly interacting systems in arbitrary dimension
• Distillation of multipartite entanglement by complementary stabilizer measurements
• Connecting the generalized robustness and the geometric measure of entanglement
• Multi-particle entanglement manipulation under positive partial transpose preserving operations
• Construction of extremal local positive operator-valued measures under symmetry

Cited by in corpus (9)

• Entanglement detection
• The geometric measure of entanglement for symmetric states
• Multiparticle entanglement under the influence of decoherence
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• Lower bounds on entanglement measures from incomplete information
• Phase transition of computational power in the resource states for one-way quantum computation
• Relative entropy of entanglement for certain multipartite mixed states
• Survival of entanglement in thermal states
• How much of one-way computation is just thermodynamics?