Indecomposable Exposed Positive Bi-linear Maps Between Two by Two Matrices



Positive bi-linear maps between matrix algebras play important roles to detect tri-partite entanglement by the duality between bi-linear maps and tri-tensor products. We exhibit indecomposable positive bi-linear maps between 2 × 2 matrices which generate extreme rays in the cone of all positive bi-linear maps. In fact, they are exposed, and so detect entanglement of positive partial transpose (PPT) whose volume is nonzero.


Positive multi-linear maps Exposed Indecomposable Separable Partial transpose 

Mathematics Subject Classification (2010)

46L07 15A30 81P15 



The author is grateful to Kyung-Hoon Han for useful discussion and comments. The author is partially supported by NRF-2017R1A2B4006655.


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Institute of MathematicsSeoul National UniversitySeoulKorea

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