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arXiv:quant-ph/0104039 · Physical Review A

Practical scheme for entanglement concentration

Zhi Zhao, Jian-Wei Pan, Mingsheng Zhan

Published Jun 4, 2001• 251 citations
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Abstract

We present a realistic purification scheme for pure nonmaximally entangled states. In the scheme, two distant parties Alice and Bob first start with two shared but less entangled photon pairs to produce a conditional four-photon Greenberger-Horne-Zeilinger state, and then perform a $45\ifmmode^\circ\else\textdegree\fi{}$ polarization measurement onto one of the two photons at each location such that the remaining two photons are projected onto a maximally entangled state.

DOI
10.1103/physreva.64.014301

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It is known that entanglement swapping can be used to realize entanglement purification. In this way, two particles belonging to different nonmaximally entangled pairs can be projected probabilistically to a maximally entangled state or to a less entangled state. In this paper, we show, when the less entangled state is obtained, then a maximally entangled state can be obtained probabilistically from this less entangled state if a unitary transformation is introduced locally. The probability of success of our scheme is equal to the entanglement of a single pair purification (if two original pairs are in the same nonmaximally entangled states) or to the smaller entanglement of a single pair purification of these two pairs (if two original pairs are not in the same nonmaximally entangled states). The advantage of our scheme is that no continuous indefinite iterative procedure is needed to achieve optimal purification.
We present two economical one-step error-correction protocols for multipartite polarization-entangled systems in a Greenberger-Horne-Zeilinger state. One uses spatial entanglement to correct errors in the polarization entanglement of an NNN-photon system, resorting to linear optical elements. The other uses frequency entanglement to correct errors in the polarization entanglement of an NNN-photon system. The parties in quantum communication can obtain a maximally entangled state from each NNN-photon system transmitted with one step in these two protocols, and both of their success probabilities are 100100%100, in principle. That is, they both work in a deterministic way, and they do not largely consume the less-entangled photon systems, which is far different from conventional multipartite entanglement purification schemes. These features may make these two protocols more useful for practical applications in long-distance quantum communication.