We consider entanglement distillation from a single copy of multipartite quantum states, and instead of rates we analyze the “quality” of the distilled entanglement. This quality is quantified by the fidelity with the gigahertz state. We show that each not fully separable state can increase the quality of the entanglement distilled from other states, no matter how weakly entangled is . We also generalize this to the case where the goal is distilling states different from the gigahertz. These results provide new insights on the geometry of the set of separable states and its dual (the set of entanglement witnesses).
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