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No pure entangled state can be distilled from a $2\otimes 2$ or $2\otimes 3$mixed state by separable operations. In $3\otimes 3$, pure entanglement can bedistilled by separable operation but not by LOCC. In this letter, we proved theconjecture [PRL. 103, 110502 (2009)] that it is possible to distill pureentanglement for $2\otimes 4$ system by LOCC and further improve these inhigher dimensions to distill a pure entangled state of Schmidt rank $d$ from a$m\otimes n$ mixed state by separable operation when $m+n \geqslant 3d$. Wefound results for tripartite systems with target state $d$-level GHZ-typestate. These results provide a class of systems where separable operation isstrictly stronger than LOCC.

Entangled state distillation from single copy mixed states beyond LOCC