Nonadditivity of Rains' bound for distillable entanglement

Abstract

Rains’ bound is arguably the best known upper bound of the distillable entanglement by operations completely preserving positivity of partial transpose (PPT) and was conjectured to be additive and coincide with the asymptotic relative entropy of entanglement. We disprove both conjectures by explicitly constructing a special class of mixed two-qubit states. We then introduce an additive semidefinite programming lower bound for the asymptotic Rains’ bound, and it immediately becomes a computable lower bound for entanglement cost of bipartite states. Furthermore, our introduced quantity is also proved to be the best known upper bound of the PPT-assisted deterministic distillable entanglement and gives the asymptotic rates for all pure states and some class of genuinely mixed states.

Publication
Physical Review A
Xin Wang
Xin Wang
Associate Professor

The main focus of my research is to better understand the limits of information processing with quantum systems and the power of quantum artificial intelligence.