Universal distillation of quantum entanglement

Abstract

Distillable entanglement---the maximum rate of Bell states extractable from the given noisy entangled states via local operations and classical communication (LOCC)---has been a central quantity to characterize the operational value of entangled states. However, this operational meaning had been known to be valid only under a crucial assumption: both parties know the description of the input state and can choose the protocol tailored to it, which does not necessarily reflect the natural operational setting. Here, we show that the distillable entanglement is the fundamental operational quantity even without this assumption. We present a universal LOCC protocol---whose description does not depend on the input state and thus works universally for any input---that achieves the distillable entanglement of an arbitrary unknown input state. Our result therefore lifts the distillable entanglement to a robust notion of an operationally meaningful quantity and clarifies that input-state knowledge is not necessary to achieve the optimal rate of entanglement distillation. Our protocol is based on state merging for compound states, together with the uniform convergence property of the finite-block quantity toward distillable entanglement.