講座內容：We study various aspects of a symptotic entanglement manipulation of general bipartite states under operations that completely preserve positivity of partial transpose (PPT). Our key findings include: i) an additive semi-definite programming (SDP) entanglement measure which is an improved upper bound of the distillable entanglement than the logarithmic negativity; ii) a succinct SDP characterization of the one-copy deterministic distillation rate and an additive upper bound; iii) non additivity of Rains’ bound for a class of two-qubit states; and iv) two additive SDP lower bounds to the Rains’ bound and relative entropy of entanglement, respectively. These findings enable us to efficiently evaluate the asymptotic distillableentanglement and entanglement cost for several classes of mixed states. As applications, we show that for any rank-two mixed state supporting on the3-level anti-symmetric subspace, both the Rains’ bound and its regularization are strictly less than the asymptotic relative entropy of entanglement. Thatalso implies the irreversibility of asymptotic entanglement manipulation under PPT operations, one of the major open problems in quantum information theory.

Joint works with Mr Xin Wang (UTS),available at arXiv:1601.07940, 1605.00348 and 1606.09421.