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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 - PowerPoint PPT Presentation
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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