Universal distortion-free entanglement concentration

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.