Randomized Graph States and their Entanglement Properties

Abstract

We introduce a class of mixed multiqubit states, that corresponds to a randomized version of graph states. Such states arise when a graph state is prepared with noisy or imperfect controlled-Z gates. We study the entanglement features of these states by investigating both bipartite and genuine multipartite entanglement. Bipartite entanglement is studied via the concepts of connectedness and persistency, which are related to measurement based quantum computation. The presence of multipartite entanglement is instead revealed by the use of witness operators which are subsequently adapted to study nonlocal properties through the violation of suitable Bell inequalities. We also present results on the entanglement detection of particular randomized graph states, by deriving explicit thresholds for entanglement and nonlocality in terms of the noise parameter that characterizes the controlled-Z gates exploited for their generation. Finally, we propose a method to further improve the detection of genuine multipartite entanglement in this class of states.

This is the published version. We have added some text to clarify our results, corrected typos in references, and made some minor style modifications according to the journal

References in corpus (6)

• Multi-party entanglement in graph states
• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Taming multiparticle entanglement
• Quantifying Entanglement with Witness Operators
• Bell Inequalities for Graph States
• Optimal preparation of graph states

Cited by in corpus (11)

• Genuine Multipartite Entanglement in the Cluster-Ising Model
• Green's function approach for quantum graphs: an overview
• Construction of multi-qubit optimal genuine entanglement witnesses
• Entanglement of random hypergraph states
• Analysis of quantum error correction with symmetric hypergraph states
• Generation of complete graph states in a spin-$1/2$ Heisenberg chain with a globally optimized magnetic field
• Group structures and representations of graph states
• Multipartite entanglement sudden death and birth in randomized hypergraph states
• Quantum transport in randomized quantum graphs
• Randomized hypergraph states and their entanglement properties
• Determining X-chains in graph states