# Entanglement witnesses for graph states: General theory and examples

## 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 1 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.

- Authors:

- Institut fuer Quantenoptik und Quanteninformation, Oesterreichische Akademie der Wissenschaften, Technikerstrasse 21A, A-6020 Innsbruck (Austria)
- (Germany)

- Publication Date:

- OSTI Identifier:
- 22068655

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 3; Other Information: (c) 2011 American Institute of Physics; Country of input: Syrian Arab Republic; Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; AUGMENTATION; NOISE; QUANTUM ENTANGLEMENT; QUBITS; TOLERANCE

### Citation Formats

```
Jungnitsch, Bastian, Moroder, Tobias, Guehne, Otfried, and Naturwissenschaftlich-Technische Fakultaet, Universitaet Siegen, Walter-Flex-Strasse 3, D-57068 Siegen.
```*Entanglement witnesses for graph states: General theory and examples*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.032310.

```
Jungnitsch, Bastian, Moroder, Tobias, Guehne, Otfried, & Naturwissenschaftlich-Technische Fakultaet, Universitaet Siegen, Walter-Flex-Strasse 3, D-57068 Siegen.
```*Entanglement witnesses for graph states: General theory and examples*. United States. doi:10.1103/PHYSREVA.84.032310.

```
Jungnitsch, Bastian, Moroder, Tobias, Guehne, Otfried, and Naturwissenschaftlich-Technische Fakultaet, Universitaet Siegen, Walter-Flex-Strasse 3, D-57068 Siegen. Thu .
"Entanglement witnesses for graph states: General theory and examples". United States. doi:10.1103/PHYSREVA.84.032310.
```

```
@article{osti_22068655,
```

title = {Entanglement witnesses for graph states: General theory and examples},

author = {Jungnitsch, Bastian and Moroder, Tobias and Guehne, Otfried and Naturwissenschaftlich-Technische Fakultaet, Universitaet Siegen, Walter-Flex-Strasse 3, D-57068 Siegen},

abstractNote = {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 1 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.},

doi = {10.1103/PHYSREVA.84.032310},

journal = {Physical Review. A},

issn = {1050-2947},

number = 3,

volume = 84,

place = {United States},

year = {2011},

month = {9}

}