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Marcin Marciniak--Positive maps and its applications in quantum information
发布人:管理员LIU  发布时间:2017-06-27   浏览次数:501

Program: 

1. Basic notions: positivty, k-(co)positivity, complete (co)positivity, decomposability

2. Basic properties: relations between k- and l- positivity for different k,l; case when domain or predomain is commutative; Stinespring form of completely positive maps

3. Stormer-Kye duality: convex structures; duality between positive maps and states on tensor product

4. Characterization of dual sets to positive, decomposable and completely positive maps as separable, PPT and all states; concept of an entanglement witness

5. Choi matrix method: Choi's theorem on characterization of completely positive maps on matrix algebras, Kraus form; Choi matrix vs duality

6. Problem of classification of positive maps: low dimensional case (Stormer, Woronowicz); examples in higher dimensional algebras; extremal and exposed maps, Straszecicz theorem; optimality

All lectures are elemetary and instroductive! 


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