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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

A concentration/purification scheme for two partially entangled photon pairs

Takashi Yamamoto, Masato Koashi, N. Imoto

Published Nov 13, 2002• 13 citations
Publisher

Abstract

An experimental scheme for concentrating entanglement in partially entangled photon pairs is proposed. A practical realization of the proposed scheme is discussed, which uses imperfect photon detectors and spontaneous parametric down-conversion as a photon source. This scheme also works for purifying a class of mixed states.
DOI
10.1109/cleopr.2001.971011

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 31, 2006•1 citation
An experimental scheme for concentrating entanglement in partially entangled photon pairs is proposed. In this scheme, two separated parties obtain one maximally entangled photon pair from two previously shared partially entangled photon pairs by local operations and classical communication. A practical realization of the proposed scheme is discussed, which uses imperfect photon detectors and spontaneous parametric down-conversion as a photon source. This scheme also works for purifying a class of mixed states.
We propose a scheme for purification of a general mixed entangled state. In this scheme, we start from a large number of general mixed entangled states and end up, after local operation and classical communication, with a smaller number of Bell diagonal states with higher entanglement. In particular, the scheme can purify one maximally entangled state from two entangled pairs prepared in a class of mixed entangled state. Furthermore we propose a linear optical implementation of the present scheme with polarization beam splitters and photon detectors.
We present an entanglement purification protocol and an entanglement concentration protocol in this paper, resorting to cross-Kerr nonlinearities and interference of two coherent beams. Our purification protocol can be used to purify photon pairs not only from an ideal entangled source but also from a parametric down-conversion source by the measurement on the interference of two coherent beams without giant cross-Kerr media. Our quantum nondemolition detection can also used to concentrate photon pairs in less entangled pure states efficiently. Our protocols are more flexibilities in distinguishing the phases of the coherent states during homodyne detection.
We present a scheme for entanglement purification with linear optics that works for currently available parametric down-conversion sources, in contrast to a previous scheme [J. W. Pan, Nature (London) 410, 1067 (2001)]] that relied on ideal single-pair sources. The present scheme makes use of spatial entanglement in order to purify polarization entanglement. Surprisingly, spatial entanglement as an additional resource also leads to a substantial improvement in entanglement output compared to the previous scheme.
We propose practical schemes for concentrating entanglement of a pair of unknown partially entangled Bell states and three-photon W states with cross-Kerr nonlinearity. In these schemes, utilizing local operations and classical communication, two separated parties can obtain one maximally entangled photon pair from two previously shared partially entangled photon pairs, and three separated parties can obtain one maximally entangled three-photon W state and a maximally entangled cluster state from two identical partially entangled three-photon W states with a certain success probability. Finally, we discuss the influence of sources of error and decoherence on the schemes. The proposed setup only employs some linear optical elements and the cross-Kerr medium, which greatly reduces the difficulty of experimental realization. These schemes are feasible with current experimental technology.