# Manipulating multiqudit entanglement witnesses by using linear programming

## Abstract

A class of entanglement witnesses (EWs) called reduction-type entanglement witnesses is introduced, which can detect some multipartite entangled states including positive partial transpose ones with Hilbert space of dimension d{sub 1}(multiply-in-circle sign)d{sub 2}(multiply-in-circle sign){center_dot}{center_dot}{center_dot}(multiply-in-circle sign)d{sub n}. In fact the feasible regions of these EWs turn out to be convex polygons and hence the manipulation of them reduces to linear programming which can be solved exactly by using the simplex method. The decomposability and nondecomposability of these EWs are studied and it is shown that it has a close connection with eigenvalues and optimality of EWs. Also using the Jamiolkowski isomorphism, the corresponding possible positive maps, including the generalized reduction maps of Hall [Phys. Rev. A 72, 022311 (2005)] are obtained.

- Authors:

- Department of Theoretical Physics and Astrophysics, Tabriz University, Tabriz 51664 (Iran, Islamic Republic of)
- (Iran, Islamic Republic of)

- Publication Date:

- OSTI Identifier:
- 20982495

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.75.052326; (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; EIGENFUNCTIONS; EIGENVALUES; HILBERT SPACE; INFORMATION THEORY; QUANTUM ENTANGLEMENT; QUANTUM INFORMATION; QUBITS

### Citation Formats

```
Jafarizadeh, M. A., Institute for Studies in Theoretical Physics and Mathematics, Tehran 19395-1795, Research Institute for Fundamental Sciences, Tabriz 51664, Najarbashi, G., Institute for Studies in Theoretical Physics and Mathematics, Tehran 19395-1795, and Habibian, H.
```*Manipulating multiqudit entanglement witnesses by using linear programming*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.052326.

```
Jafarizadeh, M. A., Institute for Studies in Theoretical Physics and Mathematics, Tehran 19395-1795, Research Institute for Fundamental Sciences, Tabriz 51664, Najarbashi, G., Institute for Studies in Theoretical Physics and Mathematics, Tehran 19395-1795, & Habibian, H.
```*Manipulating multiqudit entanglement witnesses by using linear programming*. United States. doi:10.1103/PHYSREVA.75.052326.

```
Jafarizadeh, M. A., Institute for Studies in Theoretical Physics and Mathematics, Tehran 19395-1795, Research Institute for Fundamental Sciences, Tabriz 51664, Najarbashi, G., Institute for Studies in Theoretical Physics and Mathematics, Tehran 19395-1795, and Habibian, H. Tue .
"Manipulating multiqudit entanglement witnesses by using linear programming". United States.
doi:10.1103/PHYSREVA.75.052326.
```

```
@article{osti_20982495,
```

title = {Manipulating multiqudit entanglement witnesses by using linear programming},

author = {Jafarizadeh, M. A. and Institute for Studies in Theoretical Physics and Mathematics, Tehran 19395-1795 and Research Institute for Fundamental Sciences, Tabriz 51664 and Najarbashi, G. and Institute for Studies in Theoretical Physics and Mathematics, Tehran 19395-1795 and Habibian, H.},

abstractNote = {A class of entanglement witnesses (EWs) called reduction-type entanglement witnesses is introduced, which can detect some multipartite entangled states including positive partial transpose ones with Hilbert space of dimension d{sub 1}(multiply-in-circle sign)d{sub 2}(multiply-in-circle sign){center_dot}{center_dot}{center_dot}(multiply-in-circle sign)d{sub n}. In fact the feasible regions of these EWs turn out to be convex polygons and hence the manipulation of them reduces to linear programming which can be solved exactly by using the simplex method. The decomposability and nondecomposability of these EWs are studied and it is shown that it has a close connection with eigenvalues and optimality of EWs. Also using the Jamiolkowski isomorphism, the corresponding possible positive maps, including the generalized reduction maps of Hall [Phys. Rev. A 72, 022311 (2005)] are obtained.},

doi = {10.1103/PHYSREVA.75.052326},

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}

}