Entangled state distillation from single copy mixed states beyond LOCC

TL;DR

This paper demonstrates that pure entanglement can be distilled from certain mixed states in higher-dimensional systems using LOCC and separable operations, revealing cases where separable operations outperform LOCC.

Contribution

It proves the conjecture that pure entanglement distillation is possible in 2x4 systems by LOCC and extends results to higher dimensions with separable operations, showing their superiority over LOCC.

Findings

Pure entanglement distillation in 2x4 systems by LOCC.

Separable operations can distill pure entanglement in higher dimensions.

Separable operations are strictly stronger than LOCC in certain systems.

Abstract

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 be distilled by separable operation but not by LOCC. In this letter, we proved the conjecture [PRL. 103, 110502 (2009)] that it is possible to distill pure entanglement for $2\otimes 4$ system by LOCC and further improve these in higher dimensions to distill a pure entangled state of Schmidt rank $d$ from a $m\otimes n$ mixed state by separable operation when $m+n \geqslant 3d$. We found results for tripartite systems with target state $d$-level GHZ-type state. These results provide a class of systems where separable operation is strictly stronger than LOCC.