Iran International Conference on Quantum Information Kish Island

Iran International Conference on Quantum Information Kish Island, Iran 7 -10 September 2007 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

Outline Ø Motivation Ø Entanglement Witnesses & Convex Optimization Ø Manipulating Entanglement Witnesses by Linear Programming Ø Multi-partite Entanglement Witnesses Ø Optimality, Decomposability & Positive maps Ø Conclusion

Motivation

1. Entanglement Witnesses

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

3. Manipulating EWs by LP method

4. Multi-qudit Reduction type EWs Jafarizadeh, Najarbashi, Habibian: PRA_75_052326

4. 1 Optimality and Decomposability of

Decomposable ? Non-Decomposable

4. 2 Positive Maps

5. Stabilizer EWs Jafarizadeh, Najarbashi, Akbari, Habibian, ar. Xiv: 0704. 2414 v 1

Conclusion Ø The advantage of reducing manipulation of EWs to LP problem is to find optimal (Decomposable or Nondecomposable) EWs and it leads to detect larger areas of entanglement even when we solve our problem with approximated LP ones. Thanks for your attention Ø Studying Decomposable and Non-decomposable regions in multi-partite systems are so difficult which might be simplified by this method. Ø Multi-partite EWs open a new aspects to introduce many positive maps. Nonlinear Convex Optimization