Necessary and sufficient condition for distillability with unit 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
2002 Physical Review A. Atomic, Molecular, and Optical Physics  
It is well known that any entangled mixed state in 2⊗ 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
more » ... 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.
doi:10.1103/physreva.66.022309 fatcat:53ntm2bs2fhhzndglxlfpttiba