Positive maps and its applications in quantum information

发布时间:2017-06-27浏览次数:874

Speaker: Professor Marcin Marciniak

Institution: Gdansk University

Location: Room 522, Gewu Building

Title: Positive maps and its applications in quantum information

Time: Lecture 1:2017.06.27. 15:00-16:00; Lecture 2: 2017.06.29. 15:00-16:00; Lecture 3: 2017.07.03. 15:00-16:00.

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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