# Existence criterion of genuine tripartite entanglement

## Abstract

In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits [Phys. Rev. A 61, 052306 (2000)] to the tripartite systems in higher dimension. The spirit lies in the tensor treatment of tripartite pure states [Phys. Rev. A 72, 022333 (2005)]. A distinct characteristic of the present generalization is that the formulation for higher dimensional systems is invariant under permutation of the subsystems, hence is employed as a criterion to test the existence of genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the Kronecker product approximate technique. As applications, we give the analytic approximation of the criterion for weakly mixed tripartite quantum states and consider the existence of genuine tripartite entanglement of some weakly mixed states.

- Authors:

- Department of Physics, Dalian University of Technology, Dalian 116024 (China)

- Publication Date:

- OSTI Identifier:
- 20786871

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.73.032322; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; APPROXIMATIONS; ENERGY LEVELS; MIXED STATE; QUANTUM ENTANGLEMENT; QUBITS; TENSORS

### Citation Formats

```
Yu Changshui, and Song Heshan.
```*Existence criterion of genuine tripartite entanglement*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.

```
Yu Changshui, & Song Heshan.
```*Existence criterion of genuine tripartite entanglement*. United States. doi:10.1103/PHYSREVA.73.0.

```
Yu Changshui, and Song Heshan. Wed .
"Existence criterion of genuine tripartite entanglement". United States.
doi:10.1103/PHYSREVA.73.0.
```

```
@article{osti_20786871,
```

title = {Existence criterion of genuine tripartite entanglement},

author = {Yu Changshui and Song Heshan},

abstractNote = {In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits [Phys. Rev. A 61, 052306 (2000)] to the tripartite systems in higher dimension. The spirit lies in the tensor treatment of tripartite pure states [Phys. Rev. A 72, 022333 (2005)]. A distinct characteristic of the present generalization is that the formulation for higher dimensional systems is invariant under permutation of the subsystems, hence is employed as a criterion to test the existence of genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the Kronecker product approximate technique. As applications, we give the analytic approximation of the criterion for weakly mixed tripartite quantum states and consider the existence of genuine tripartite entanglement of some weakly mixed states.},

doi = {10.1103/PHYSREVA.73.0},

journal = {Physical Review. A},

number = 3,

volume = 73,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}