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IEEE International Symposium on Information Theory (ISIT)

Universal distortion-free entanglement concentration

Keiji Matsumoto, Masahito Hayashi

Published Dec 23, 2004• 9 citations
Publisher

Abstract

This paper proposes a universal distortion-free entanglement concentration protocol. The proposed protocol uses only local operations and no classical communication, but still achieves optimality in such strong senses
DOI
10.1109/isit.2004.1365360

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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 nnn-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.
Using invariance of the nnn-th tensored state w.r.t. the nnn-th symmetric group, we propose a 'variable length' universal entanglement concentration without classical communication. Like variable length data compression, arbitrary unknown states are concentrated into perfect Bell states and not approximate Bell states and the number of Bell states obtained is equal to the optimal rate asymptotically with the probability 1. One of the point of our scheme is that we need no classical communication at all. Using this method, we can construct a universal teleportation and a universal dense coding.