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According to the map of a qubit, a scheme for protecting entanglement of two-qubit by the weak measurements at finite temperature is proposed. Since the choices of the channel parameters and initial states are very different for different weak measurement strengths, two local unitary equivalent initial entangled states |ψ> and |φ> are chosen. Weak measurements are performed when two initial entangled states go through the generalized amplitude damping channel, and the analytical expressions of getting maximum concurrence entanglement Cr and weak measurement parameters m and n can be obtained by performing an overall optimization for four weak measurement parameters. What is more, the relationship between the weak measurement parameters and the channel parameters is further explored. Theoretical results show the entanglement protection project based on weak measurements can effectively enhance the entanglement and even prevent the sudden death of entanglement in some cases. When the channel parameter r is fixed, for different values of parameter p, the concurrence is centered at p = 0.5, and the weak measurement parameters of the maximum concurrence entanglement are the same as those for initial state |ψ>, while they are different for initial state |φ>. Under the condition of different values of r, for the fixed p and initial state |ψ> or |φ>, the weak measurement parameters remain constant as the entanglement reaches the maximum and the concurrence decreases with the increase of parameter r. Through the analysis of channel parameters, higher entanglement can be obtained by choosing appropriate channel parameters and initial state.
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Keywords:
- decoherence /
- entanglement /
- weak measurement
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[7] Wang X W, Zhang D Y, Tang S Q, You K M 2010 Int. J. Theor. Phys. 49 2691
[8] Wang X W, Zhang D Y, Tang S Q, Xie L J 2011 J. Phys. B: At. Mol. Opt. Phys. 44 035505
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[10] Yan L H, Gao Y F, Zhao J G A 2009 Int. J. Theor. Phys. 48 2445
[11] Wang X W, Yang G J 2009 Phys. Rev. A 79 064306
[12] Fan H, Wang Y N, Jing L, Yue J D, Shi H D, Zhang Y L, Mu L Z 2014 Phys. Rep. 544 241
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[14] Wang X W, Zhang D Y, Yang G J, Tang S Q, Xie L J 2011 Phys. Rev. A 84 042310
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[16] Xu P, Wang D, Ye L 2013 Chin. Phys. B 22 100306
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[19] Zurek W H 2003 Rev. Mod. Phys. 75 715
[20] Yu T, Eberly J H 2004 Phys. Rev. Lett. 93 140404
[21] Almeida M P, de Melo F, Hor-Meyll M, Salles A, Walborn S P, Ribeiro P H S, Davidovich L 2007 Science 316 579
[22] Yu T, Eberly J H 2007 Phys. Rev. Lett. 97 140403
[23] Almeida M P, de Melo F, Hor-Meyll M, Salles A, Walborn S P, Ribeiro P H S, Davidovich L 2007 Science 316 579
[24] Eberly J H, Yu T 2007 Science 316 555
[25] Shor P W 1995 Phys. Rev. A 52 R2493
[26] Steane A M 1996 Phys. Rev. Lett. 77 793
[27] Lidar D A, Chuang I L, Whaley K B 1998 Phys. Rev. Lett. 81 2594
[28] Kwiat P G, Berglund A J, Altepeter J B, White A G 2000 Science 290 498
[29] Viola L, Knill E, Lloyd S 1999 Phys. Rev. Lett. 82 2417
[30] West J R, Lidar D A, Fong B H, Gyure M F 2010 Phys. Rev. Lett. 105 230503
[31] He Z, Yao C M 2014 Chin. Phys. B 23 110601
[32] Han W, Zhang Y J, Yan W B, Xia Y J 2014 Chin. Phys. B 23 0110304
[33] Kim Y S, Lee J C, Kwon O, Kim Y H 2011 Nat. Phys. 10 1038
[34] Sun Q Q, Al-Amri M, Davidovich L, Zubairy M S 2010 Phys. Rev. A 82 052323
[35] Man Z X, Xia Y J 2012 Phys. Rev. A 86 012325
[36] Man Z X, Xia Y J 2012 Phys. Rev. A 86 052322
[37] Liao X P, Fang M F, Fang J S, Zhu Q Q 2013 Chin. Phys. B 23 020304
[38] Xiao X 2014 Phys. Scr. 89 065102
[39] Wang S C, Yu Z W, Zou W J, Wang X B 2014 Phys. Rev. A 89 022318
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[1] Nielsen M, Chuang I 2000 Quantum Information and Computation (Cambridge: Cambridge University Press) pp171-593
[2] Bennett C H, Brassard G, Crepeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[3] Song J, Xia Y, Song H S 2008 Phys. Rev. A 78 024302
[4] Liu J C, Li Y H, Nie Y Y 2010 Int. J. Theor. Phys. 49 1976
[5] Jennewein T, Weihs G, Pan J W, Zeilinger A 2001 Phys. Rev. Lett. 88 017903
[6] Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1829
[7] Wang X W, Zhang D Y, Tang S Q, You K M 2010 Int. J. Theor. Phys. 49 2691
[8] Wang X W, Zhang D Y, Tang S Q, Xie L J 2011 J. Phys. B: At. Mol. Opt. Phys. 44 035505
[9] Murao M, Jonathan D, Plenio M B, Vedral V 1999 Phys. Rev. A 59 156
[10] Yan L H, Gao Y F, Zhao J G A 2009 Int. J. Theor. Phys. 48 2445
[11] Wang X W, Yang G J 2009 Phys. Rev. A 79 064306
[12] Fan H, Wang Y N, Jing L, Yue J D, Shi H D, Zhang Y L, Mu L Z 2014 Phys. Rep. 544 241
[13] Murao M, Vedral V 2001 Phys. Rev. Lett. 86 352
[14] Wang X W, Zhang D Y, Yang G J, Tang S Q, Xie L J 2011 Phys. Rev. A 84 042310
[15] Zhang Y J, Zhou Y, Xia Y J 2008 Acta Phys. Sin. 57 21 (in Chinese) [张英杰, 周原, 夏云杰 2008 物理学报 57 21]
[16] Xu P, Wang D, Ye L 2013 Chin. Phys. B 22 100306
[17] Horodedecki R, Horodedecki P, Horodedecki M, Horodedecki K 2009 Rev. Mod. Phys. 81 865
[18] Zyczkowski K, Horodedecki P, Horodedecki M, Horodedecki R 2001 Phys. Rev. A 65 012101
[19] Zurek W H 2003 Rev. Mod. Phys. 75 715
[20] Yu T, Eberly J H 2004 Phys. Rev. Lett. 93 140404
[21] Almeida M P, de Melo F, Hor-Meyll M, Salles A, Walborn S P, Ribeiro P H S, Davidovich L 2007 Science 316 579
[22] Yu T, Eberly J H 2007 Phys. Rev. Lett. 97 140403
[23] Almeida M P, de Melo F, Hor-Meyll M, Salles A, Walborn S P, Ribeiro P H S, Davidovich L 2007 Science 316 579
[24] Eberly J H, Yu T 2007 Science 316 555
[25] Shor P W 1995 Phys. Rev. A 52 R2493
[26] Steane A M 1996 Phys. Rev. Lett. 77 793
[27] Lidar D A, Chuang I L, Whaley K B 1998 Phys. Rev. Lett. 81 2594
[28] Kwiat P G, Berglund A J, Altepeter J B, White A G 2000 Science 290 498
[29] Viola L, Knill E, Lloyd S 1999 Phys. Rev. Lett. 82 2417
[30] West J R, Lidar D A, Fong B H, Gyure M F 2010 Phys. Rev. Lett. 105 230503
[31] He Z, Yao C M 2014 Chin. Phys. B 23 110601
[32] Han W, Zhang Y J, Yan W B, Xia Y J 2014 Chin. Phys. B 23 0110304
[33] Kim Y S, Lee J C, Kwon O, Kim Y H 2011 Nat. Phys. 10 1038
[34] Sun Q Q, Al-Amri M, Davidovich L, Zubairy M S 2010 Phys. Rev. A 82 052323
[35] Man Z X, Xia Y J 2012 Phys. Rev. A 86 012325
[36] Man Z X, Xia Y J 2012 Phys. Rev. A 86 052322
[37] Liao X P, Fang M F, Fang J S, Zhu Q Q 2013 Chin. Phys. B 23 020304
[38] Xiao X 2014 Phys. Scr. 89 065102
[39] Wang S C, Yu Z W, Zou W J, Wang X B 2014 Phys. Rev. A 89 022318
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