# Multipartite unlockable bound entanglement in the stabilizer formalism

## Abstract

We find an interesting relationship between multipartite bound entangled states and the stabilizer formalism. We prove that, if a set of commuting operators from the generalized Pauli group on n qudits satisfy certain constraints, then the maximally mixed state over the subspace stabilized by them is an unlockable bound entangled state. Moreover, the properties of this state, such as symmetry under permutations of parties, undistillability, and unlockability, can be easily explained from the stabilizer formalism without tedious calculation. In particular, the four-qubit Smolin state [Smolin, Phys. Rev. A 63, 032306 (2001)] and its recent generalization to even numbers of qubits [Bandyopadhyay et al., Phys. Rev. A 71, 062317 (2005); Augusiak et al., ibid 73, 012318 (2006)] can be viewed as special examples of our results. Finally, we extend our results to arbitrary multipartite systems in which the dimensions of all parties may be different.

- Authors:

- State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing 100084 (China)

- Publication Date:

- OSTI Identifier:
- 20982501

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.75.052332; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; INFORMATION THEORY; MIXED STATE; PAULI PRINCIPLE; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUBITS; SYMMETRY

### Citation Formats

```
Wang, Guoming, and Ying, Mingsheng.
```*Multipartite unlockable bound entanglement in the stabilizer formalism*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.052332.

```
Wang, Guoming, & Ying, Mingsheng.
```*Multipartite unlockable bound entanglement in the stabilizer formalism*. United States. doi:10.1103/PHYSREVA.75.052332.

```
Wang, Guoming, and Ying, Mingsheng. Tue .
"Multipartite unlockable bound entanglement in the stabilizer formalism". United States.
doi:10.1103/PHYSREVA.75.052332.
```

```
@article{osti_20982501,
```

title = {Multipartite unlockable bound entanglement in the stabilizer formalism},

author = {Wang, Guoming and Ying, Mingsheng},

abstractNote = {We find an interesting relationship between multipartite bound entangled states and the stabilizer formalism. We prove that, if a set of commuting operators from the generalized Pauli group on n qudits satisfy certain constraints, then the maximally mixed state over the subspace stabilized by them is an unlockable bound entangled state. Moreover, the properties of this state, such as symmetry under permutations of parties, undistillability, and unlockability, can be easily explained from the stabilizer formalism without tedious calculation. In particular, the four-qubit Smolin state [Smolin, Phys. Rev. A 63, 032306 (2001)] and its recent generalization to even numbers of qubits [Bandyopadhyay et al., Phys. Rev. A 71, 062317 (2005); Augusiak et al., ibid 73, 012318 (2006)] can be viewed as special examples of our results. Finally, we extend our results to arbitrary multipartite systems in which the dimensions of all parties may be different.},

doi = {10.1103/PHYSREVA.75.052332},

journal = {Physical Review. A},

number = 5,

volume = 75,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}