FIG. 2: Upper bound of F ( ρ ) from (21) (solid line) and single fraction of entanglement F$_{s}$ Acknowledgments This work is supported by NSFC 10675086, 10875081, 10871227, KZ200810028013 and NKBRPC(2004CB318000). [1] M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, (2000). [2] See, for example, D.P. Di Vincenzo, Science 270,255(1995) [3] C.H. Bennett, G. Brassard, C. Cr´ epeau, R. Jozsa, A. Peres and W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993); S. Albeverio and S.M. Fei, Phys.Lett. A 276, 8(2000); G.M. D’Ariano, P. Lo Presti and M.F. Sacchi, Phys. Lett. A 272, 32(2000). [4] S. Albeverio, S.M. Fei and W.L. Yang, Phys. Rev. A 66, 012301(2002). [5] C.H. Bennett and S.J. Wiesner, Phys. Rev. Lett. 69 , 2881(1992). [6] A. Ekert, Phys. Rev. Lett. 67, 661(1991); D. Deutsch, A. Ekert, P. Rozas, C. Macchicavello, S. Popescu and A. Sanpera, Phys. Rev. Lett. 77, 2818(1996); C.A. Fuchs, N. Gisin, R.B. Griffiths, C.S. Niu and A. Peres, Phys. Rev. A 56, 1163(1997). [7] M. ˙ Zukowski, A. Zeilinger, M.A. Horne and A.K. Ekert, Phys. Rev. Lett. 71, 4287(1993); 7 0 0.2 0.4 0.6 0.8 1 p$_{GLYPH<Equal>}$0.80 0.6 0.7 0.8 0.9 1 Bound 0 0.2 0.4 0.6 0.8 1 p$_{GLYPH<Equal>}$0.90 0.7 0.8 0.9 1 Bound 0 0.2 0.4 0.6 0.8 1 p$_{GLYPH<Equal>}$0.99 0.7 0.75 0.8 0.85 0.9 0.95 1 Bound