Abstract
We show that a bipartite quantum state of rank four is distillable if its partial transpose has at least one negative eigenvalue; that is, the state is a non-positive-partial transpose (NPT). For this purpose we prove that if the partial transpose of a two-qutrit NPT state has at least two non-positive eigenvalues, then the state is distillable. We further construct a parametrized two-qutrit NPT state of rank five which is not 1-distillable and show that it is not -distillable for any given when the parameter is sufficiently small. This state has the smallest rank among all 1-undistillable NPT states. We conjecture that the state is not distillable.
- Received 27 August 2016
DOI:https://doi.org/10.1103/PhysRevA.94.052318
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