Title: Manipulating Multi-partite Entanglement Witnesses by using Linear

Programming

By: M.A. Jafarizadeh, G. Najarbashi, Y. Akbari,

Hessam Habibian

Department of Theoretical Physics and Astrophysics, Tabriz University, Tabriz 51664, Iran

Iran International Conference on Iran International Conference on Quantum InformationQuantum Information

Kish Island, Iran 7-10 September Kish Island, Iran 7-10 September 20072007

Outline

Motivation

Entanglement Witnesses & Convex Optimization

Manipulating Entanglement Witnesses by Linear Programming

Multi-partite Entanglement Witnesses

Optimality, Decomposability & Positive maps

Conclusion

nddd ...21

Motivation

1. Entanglement Witnesses

Bounded entangled states(BES) which can be detected by Non-Decomposable EWs but not PPT criteria.

NPPT

PPT

separable

2W

1W

3. Manipulating EWs by LP method

4. Multi-qudit Reduction type EWs ) ( n21 d...dd Jafarizadeh, Najarbashi, Habibian: PRA_75_052326

4.1 Optimality and Decomposability of

Decomposable

?

Non-Decomposable

2

1

4.2 Positive Maps

5. Stabilizer EWs Jafarizadeh, Najarbashi, Akbari, Habibian, arXiv: 0704.2414v1

Nonlinear Convex Optimization

Conclusion

The advantage of reducing manipulation of EWs to LP problem is to find optimal (Decomposable or Non-decomposable) EWs and it leads to detect larger areas of entanglement even when we solve our problem with approximated LP ones.

Studying Decomposable and Non-decomposable regions in multi-partite systems are so difficult which might be simplified by this method.

Multi-partite EWs open a new aspects to introduce many positive maps.

Thanks for your

attention