Xin Wang: Asymptotic entanglement manipulation under PPT operations: new SDP bounds&irreversibility

Опубликовано 1 февраля 2017, 1:03

We study various aspects of asymptotic entanglement manipulation of general bipartite states under operations that completely preserve positivity of partial transpose (PPT). Our key findings include: i) nonadditivity of Rains' bound for a class of two-qubit states; and ii) two additive SDP lower bounds to the Rains' bound and relative entropy of entanglement, respectively. These findings enable us to better evaluate the distillable entanglement and entanglement cost. As applications, we show that for any rank-two mixed state supporting on the 3-level anti-symmetric subspace, both the Rains' bound and its regularization are strictly less than the asymptotic relative entropy of entanglement. That also implies the irreversibility of asymptotic entanglement manipulation under PPT operations, one of the major open problems in quantum information theory. We further present an SDP-computable sufficient condition for the irreversibility under PPT operations.