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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
 Motivation
 Entanglement Witnesses & Convex Optimization
 Manipulating Entanglement Witnesses by Linear Programming
 Multi-partite d1  d 2  ...  d n Entanglement Witnesses
 Optimality, Decomposability & Positive maps
 Conclusion
Motivation
1. Entanglement Witnesses
NPPT
W1
separable
PPT
W2
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 ( d1  d 2  ...  dn )
Jafarizadeh, Najarbashi, Habibian: PRA_75_052326
4.1 Optimality and Decomposability of
2
Decomposable

?
Non-Decomposable
1
4.2 Positive Maps
5. Stabilizer EWs
Jafarizadeh, Najarbashi, Akbari, Habibian, arXiv: 0704.2414v1
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.
Thanks for
your attention
 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.
Nonlinear Convex Optimization