Preserving entanglement and the fidelity of three-qubit quantum states undergoing decoherence using weak measurement

doi:10.1088/1674-1056/23/2/020304

Abstract We demonstrate a method to preserve entanglement and improve fidelity of three-qubit quantum states undergoing amplitude-damping decoherence using weak measurement and quantum measurement reversal. It is shown that we are able to enhance entanglement to the greatest extent, and to circumvent entanglement sudden death by increasing the weak measurement strength both for the GHZ state and the W state. The weak measurement technique can also enhance the fidelity to the quantum region and even close to 1 for the whole range of the decoherence parameter in both of the two cases. In addition, the W state can maintain more fidelity than the GHZ state in the protection protocol. However, the GHZ state has a higher success probability than the W state.

Keywords: entanglement protection quantum fidelity weak measurement

Received: 16 April 2013
Revised: 17 July 2013
Accepted manuscript online:

PACS:	03.65.Ud	(Entanglement and quantum nonlocality)
	42.50.Dv	(Quantum state engineering and measurements)
	03.67.Lx	(Quantum computation architectures and implementations)
	03.67.Hk	(Quantum communication)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11074072), the Natural Science Foundation of Hunan Province of China (Grant No. 10JJ3088), the Major Program for the Research Foundation of the Education Bureau of Hunan Province of China (Grant No. 10A026), and the Program for the Research Foundation of the Education Bureau of Hunan Province of China (Grant No. 10C0658).

Corresponding Authors: Liao Xiang-Ping, Fang Jian-Shu
E-mail: Liaoxp1@126.com;fjs289@163.com

About author: 03.65.Ud; 42.50.Dv; 03.67.Lx; 03.67.Hk

Cite this article:

Liao Xiang-Ping (廖湘萍), Fang Mao-Fa (方卯发), Fang Jian-Shu (方见树), Zhu Qian-Quan (朱钱泉) Preserving entanglement and the fidelity of three-qubit quantum states undergoing decoherence using weak measurement 2014 Chin. Phys. B 23 020304

[1]	Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
[2]	Gisin N, Ribordy G, Tittel W and Zbinden H 2002 Rev. Mod. Phys. 74 145
[3]	Masanes L, Pironio S and Acin A 2011 Nat. Commun. 2 238
[4]	Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A and Wootters W K 1993 Phys. Rev. Lett. 70 1895
[5]	Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H and Zeilinger A 1997 Nature 390 575
[6]	Kim Y H, Kulik S P and Shih Y H 2001 Phys. Rev. Lett. 86 1370
[7]	Giovannetti V, Lloyd S and Maccone L 2011 Nat. Photon. 5 222
[8]	Hillery M, Bužek V and Berthiaume A 1999 Phys. Rev. A 59 1829
[9]	Wang X W, Zhang D Y, Tang S Q, Zhan X G and You K M 2010 Int. J. Theor. Phys. 49 2691
[10]	Wang X W, Zhang D Y, Tang S Q and Xie L J 2011 J. Phys. B: At. Mol. Opt. Phys. 44 035505
[11]	Xu J S, Xu X Y, Li C F, Zhang C J, Zou X B and Guo G C 2010 Nat. Commun. 1 7
[12]	Cui J, Gu M, Kwek L C, Santos M F, Fan H and Vedral V 2012 Nat. Commun. 3 812
[13]	Mazzola L, Bellomo B, Franco R L and Compagno G 2010 Phys. Rev. A 81 052116
[14]	Bellomo B, Compagno G, D’Arrigo A, Falci G, Franco R L and Paladino E 2010 Phys. Rev. A 81 062309
[15]	Bellomo B, Compagno G, Franco R L, Ridolfo A and Savasta S 2011 Phys. Scr. T 143 014004
[16]	Franco R L, Bellomo B, Andersson E and Compagno G 2012 Phys. Rev. A 85 032318
[17]	Liao X P, Fang J S and Fang M F 2010 Chin. Phys. B 19 094203
[18]	Pan C N, Li F, Fang J S and Fang M F 2011 Chin. Phys. B 20 020304
[19]	Lu D M 2011 Acta Phys. Sin. 60 120303 (in Chinese)
[20]	Xu J Z, Guo J B, Wen W, Bai Y K and Yan F L 2012 Chin. Phys. B 21 080305
[21]	Wang S J and Lu P 2009 Acta Phys. Sin. 58 5955 (in Chinese)
[22]	Shor P W 1995 Phys. Rev. A 52 2493
[23]	Steane A M 1996 Phys. Rev. Lett. 77 793
[24]	Calderbank A R and Shor P W 1996 Phys. Rev. A 54 1098
[25]	Steane A M 1996 Proc. R. Soc. Lond. A 452 2551
[26]	Bellomo B, Franco R L, Maniscalco S and Compagno G 2008 Phys. Rev. A 78 060302
[27]	Bellomo B, Franco R L, Maniscalco S and Compagno G 2010 Phys. Scr. T 140 014014
[28]	Franco R L, Bellomo B, Maniscalco S and Compagno G 2013 Int. J. Mod. Phys. B 27 1345053
[29]	D’Arrigo A, Franco R L, Benenti G, Paladino E and Falci G 2012 arXiv: 1207.3294v1 [quant-ph]
[30]	Lu D M 2010 Acta Phys. Sin. 59 8359 (in Chinese)
[31]	Shan C J, Liu J B, Chen T, Liu T K, Huang Y X and Li H 2010 Acta Phys. Sin. 59 6799 (in Chinese)
[32]	Liu J M, Guo G C and Li J 2002 Chin. Phys. 11 339
[33]	Koashi M and Ueda M 1999 Phys. Rev. Lett. 82 2598
[34]	Korotkov A N and Jordan A N 2006 Phys. Rev. Lett. 97 166805
[35]	Kim Y S, Cho Y W, Ra Y S and Kim Y H 2009 Opt. Express 17 11978
[36]	Lee J C, Jeong Y C, Kim Y S and Kim Y H 2011 Opt. Express 19 16309
[37]	Kim Y S, Lee J C, Kwon O and Kim Y H 2012 Nat. Phys. 8 117
[38]	Man Z X, Xia Y J and An N B 2012 Phys. Rev. A 86 052322
[39]	Dür W, Vidal G and Cirac J I 2000 Phys. Rev. A 62 062314
[40]	Karlsson A and Bourennane M 1998 Phys. Rev. A 58 4394
[41]	Agrawal P and Pati A 2006 Phys. Rev. A 74 062320
[42]	Carmichael H 1993 An Open Systems Approach to Quantum Optics (Berlin: Springer)
[43]	Kraus K 1983 States, Effects and Operations (Berlin: Springer-Verlag)
[44]	Sabín C and García-Alcaine G 2008 Eur. Phys. J. D 48 435
[45]	Vidal G and Werner R F 2002 Phys. Rev. A 65 032314
[46]	Ou Y C and Fan H 2007 Phys. Rev. A 75 062308
[47]	Jung E, Hwang M R, Ju Y H, Kim M S, Yoo S K, Kim H, Park D K, Son J W, Tamaryan S and Cha S K 2008 Phys. Rev. A 78 012312
[48]	Hu M L 2012 arXiv: 1202.4546v2 [quant-ph]

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Preserving entanglement and the fidelity of three-qubit quantum states undergoing decoherence using weak measurement

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