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According to the Nielsens theorem and the basic idea of entanglement concentration, we improve and extend the deterministic entanglement concentration protocol that extracts one pair of maximally entangled particles out of two pairs of non-maximally entangled particles, thus establishing a deterministic entanglement concentration protocol that extracts two pairs of maximally entangled particles out of three pairs of non-maximally entangled particles in the way of the classical communication and local operation and the specific positive operator-valued measure. This is helpful for establishing a deterministic entanglement concentration protocol that extracts k pairs of maximally entangled particles out of n pairs of non-maximally entangled particles.
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[1] Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[2] Ren J G, Yang B, Yi Z H, Zhou F, Chen K, Peng C Z, Pan J W 2009 Chin. Phys. B 18 3605
[3] Chen Q, Fang X M 2008 Chin. Phys. B 17 1587
[4] Shi Z G, Chen X W, Zhu X X, Song K H 2009 Chin. Phys. B 18 910
[5] Liang B L, Wang J S 2007 Chin. Phys. 16 3097
[6] Noh T G 2009 Phys. Rev. Lett. 103 230501
[7] Werner A H, Franz T, Werner R F 2009 Phys. Rev. Lett. 103 220504
[8] Cao H J, Guo Y Q, Song H S 2006 Chin. Phys. 15 915
[9] Brunner N, Gisin N, Popescu S, Scarani V 2008 Phys. Rev. A 78 052111
[10] Zhou X Q, Lu C Y, Gao W B, Zhang J, Chen Z B, Yang T, Pan J W 2008 Phys. Rev. A 78 012112
[11] Sheng Y B, Deng F G, Zhou H Y 2008 Phys. Rev. A 77 062325
[12] Xue P, Li C F, Guo G C 2001 Phys. Rev. A 64 032305
[13] Groisman B, Linden N, Popescu S 2005 Phys. Rev. A 72 062322
[14] Ogden C D, Paternostro M, Kim M S 2007 Phys. Rev. A 75 042325
[15] Ballester D 2009 Phys. Rev. A 79 062317
[16] Short A J 2009 Phys. Rev. Lett. 102 180502
[17] Sheng Y B, Deng F G 2010 Phys. Rev. A 81 032307
[18] Reichle R, Leibfried D, Knill E, Britton J, Blakestad R B, Jost J D, Langer C, Ozeri R, Seidelin S, Wineland D J 2006 Nature 443 838
[19] Dong R, Lassen M, Heersink J, Marquardt C, Filip R, Leuchs G, Andersen U L 2008 Nat. Phys. 4 919
[20] Hage B, Samblowski A, DiGuglielmo J, Franzen A, Fiurek J, Schnabel R 2008 Nat. Phys. 4 915
[21] Takahashi H, Neergaard-Nielsen J S, Takeuchi M, Takeoka M, Hayasaka K, Furusawa A, Sasaki M 2010 Nat. Photon. 4 178
[22] Gu Y J, Li W D, Guo G C 2006 Phys. Rev. A 73 022321
[23] Wang H F, Zhang S 2009 Int. J. Theor. Phys. 48 1678
[24] Nielsen M A 1999 Phys. Rev. Lett. 83 436
[25] Morikoshi F, Koashi M 2001 Phys. Rev. A 64 022316
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