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根据单量子比特的映射, 提出一个在有限温度下运用弱测量保护两量子比特纠缠的方案. 在两个可通过局域幺正变化实现的等价的初始纠缠进入广义振幅阻尼信道前后, 对其分别进行弱测量, 并对四个弱测量的参数做全面的优化, 获取最大共生纠缠Cr 和弱测量参数m, n的解析表达式, 然后再进一步研究弱测量参数与信道参数的关系. 发现这种基于弱测量的纠缠保护方法在某些情况下可以有效地提高纠缠, 甚至可以避免纠缠的突然死亡. 当信道参数r一定时, 对不同的参数p,初始态|ψ>纠缠达到最大值时对应的弱测量参数m的取值一样, 共生纠缠关于p=0.5对称, 而初始态|φ>对应的参数m的取值不同; 在参数p一定、参数r不同、初始态|ψ>或|φ>的情况下, 当纠缠度取最大值时, 弱测量参数m的取值不变, 且随着r的增加, 纠缠度减少. 通过对信道参数的分析, 发现可以选择合适的信道参数和初始态来获得较大的纠缠.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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[24] Eberly J H, Yu T 2007 Science 316 555
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[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
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[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
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[38] Xiao X 2014 Phys. Scr. 89 065102
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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 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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