Positive maps on operator algebras – some problems and some solutions

Abstract: In the last decade, the theory of positive maps on operator algebras has gained increased importance as it has been shown to have numerous applications in quantum information theory. We will present an overview of the basic topics of this theory, in particular the characterization of extreme positive maps or the problem of decomposability. One of the intensively studied recently problems is the question of the existence of entangled PPT states with high Schmidt number. In the language of positive maps, this is equivalent to the existence of indecomposable k-positive maps for large values of k.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

Noncommutative Geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click sju.webex.com/meet/nikolaei (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.