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A Necessary And Sufficient Condition of Distillability with unite fidelity from Finite Copies of a Mixed State: The Most Efficient Purification Protocol

Ping-Xing Chen·Lin-Mei Liang·Cheng-Zu Li·Ming-Qiu Huang
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Abstract

It is well known that any entangled mixed state in $2\otimes 2$ systems can be purified via infinite copies of the mixed state. But can one distill a pure maximally entangled state from finite copies of a mixed state in any bipartite system by local operation and classical communication? This is more meaningful in practical application. We give a necessary and sufficient condition of this distillability. This condition can be expressed as: there exists distillable-subspaces. According to this condition, one can judge whether a mixed state is distillable or not easily. We also analyze some properties of distillable-subspaces, and discuss the most efficient purification protocols. Finally, we discuss the distillable enanglement of two-quibt system for the case of finite copies.

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Ping-Xing Chen, Lin-Mei Liang, Cheng-Zu Li, Ming-Qiu Huang. 2002-12-19. A Necessary And Sufficient Condition of Distillability with unite fidelity from Finite Copies of a Mixed State: The Most Efficient Purification Protocol. https://doi.org/10.1103/physreva.66.022309

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