Universal distortion-free entanglement concentration

TL;DR

This paper introduces a universal entanglement concentration protocol that achieves the optimal entropy rate and produces perfect maximally entangled states from unknown pure states, leveraging symmetry and statistical estimation.

Contribution

It presents a new protocol for entanglement concentration that is both universal and distortion-free, optimal in failure probability, and based on symmetry and estimation theory.

Findings

Achieves entropy rate for entanglement concentration.

Produces perfect maximally entangled states.

Proven optimality using statistical estimation theory.

Abstract

Entanglement concentration from many copies of unknown pure states is discussed, and we propose the protocol which not only achieves entropy rate, but also produces the perfect maximally entangled state. Our protocol is induced naturally from symmetry of $n$-tensored pure state, and is optimal for all the protocols which concentrates entanglement from unknown pure states, in the sense of failure probability. In the proof of optimality, the statistical estimation theory plays a key role, for concentrated entanglement gives a natural estimate of the entropy of entanglement.