Semi-definite programming and min-conditional entropy

In this video, I first talk about how one obtains the SDP form of the problem as a subclass of conic programming by just realizing that the cone is a set of positive semi-definite matrices. Then I discuss what min-conditional entropy is and how to frame the primal and dual problem of min-conditional entropy. I also discuss how strong duality holds and convert min conditional entropy to a new form of maximal achievable singlet fraction by allowing only local operations on one of the parties. I also talk about how the adjoint of a completely positive unital map is a completely positive trace-preserving map.
(#quantuminformation #quantum #conicprograms #maths #physics)