Quantum cloning machines and their implementation in physical systems

doi:10.1088/1674-1056/22/11/110311

Abstract We review the basic theory of approximate quantum cloning for discrete variables and some schemes for implementing quantum cloning machines. Several types of approximate quantum clones and their expansive quantum clones are introduced. As for the implementation of quantum cloning machines, we review some design methods and recent experimental results.

Keywords: quantum cloning machine discrete-variable expansive quantum clone implementation

Received: 12 September 2013
Revised: 08 October 2013
Accepted manuscript online:

PACS:	03.67.-a	(Quantum information)
	03.65.-w	(Quantum mechanics)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11074002, 61275119, and 11247009) and the Doctoral Foundation of the Ministry of Education of China (Grant No. 20103401110003).

Corresponding Authors: Ye Liu
E-mail: yeliu@ahu.edu.cn

Cite this article:

Wu Tao (吴韬), Fang Bao-Long (方保龙), Ye Liu (叶柳) Quantum cloning machines and their implementation in physical systems 2013 Chin. Phys. B 22 110311

[1]	Wootters W K and Zurek W H 1982 Nature 299 802
[2]	Bužek V and Hillery M 1996 Phys. Rev. A 54 1844
[3]	Gisin N and Massar S 1997 Phys. Rev. Lett. 79 2153
[4]	Werner R F 1998 Phys. Rev. A 58 1827
[5]	Bruss D, Ekert A and Macchiavello C 1998 Phys. Rev. Lett. 81 2598
[6]	Bruß D, DiVincenzo D P, Ekert A, Fuchs C A, Macchiavello C and Smolin J A 1998 Phys. Rev. A 57 2368
[7]	Duan L M and Guo G C 1998 Phys. Rev. Lett. 80 4999
[8]	Duan L M and Guo G C 1998 Phys. Lett. A 243 261
[9]	Scarani V, Iblisdir S, Gisin N and Acín A 2005 Rev. Mod. Phys. 77 1225
[10]	Buzek V and Hillery M 1998 Phys. Rev. Lett. 81 5003
[11]	Cerf N J 2000 Phys. Rev. Lett. 84 4497
[12]	Ghiu I 2003 Phys. Rev. A 67 012323
[13]	Gisin N and Massar S 1997 Phys. Rev. Lett. 79 2153
[14]	Werner R F 1998 Phys. Rev. A 58 1827
[15]	Bruss D, Cinchetti M, D’Ariano G M and Macchiavello C 2000 Phys. Rev. A 62 012302
[16]	Fan H, Imai H, Matsumoto K and Wang X B 2003 Phys. Rev. A 67 022317
[17]	Bartkiewicz K, Miranowicz A and Özdemir Ş K 2009 Phys. Rev. A 80 032306
[18]	Navez P and Cerf N J 2003 Phys. Rev. A 68 032313
[19]	Cerf N J 2000 J. Mod. Opt. 47 187
[20]	Han Y J, Zhang Y S and Guo G C 2002 Phys. Rev. A 66 052301
[21]	Durt T and Du J 2004 Phys. Rev. A 69 062316
[22]	Fan H, Matsumoto K, Wang X B and Wadati M 2001 Phys. Rev. A 65 012304
[23]	D’Ariano G M and Macchiavello C 2003 Phys. Rev. A 67 042306
[24]	Niu C S and Griffiths R B 1999 Phys. Rev. A 60 2764
[25]	Durt T, Fiurášek J and Cerf N 2005 Phys. Rev. A 72 052322
[26]	Fiurášek J 2003 Phys. Rev. A 67 052314
[27]	Buscemi F, D’Ariano G M and Macchiavello C 2005 Phys. Rev. A 71 042327
[28]	Delgado Y, Lamata L, León J, Salgado D and Solano E 2007 Phys. Rev. Lett. 98 150502
[29]	Zhang W H, Wu T, Ye L and Dai J L 2007 Phys. Rev. A 75 044303
[30]	Lamoureux L P, Navez P, Fiurášek J and Cerf N J 2004 Phys. Rev. A 69 040301
[31]	Karpov E, Navez P and Cerf N J 2005 Phys. Rev. A 72 042314
[32]	Fiurášek J, Iblisdir S, Massar S and Cerf N J 2002 Phys. Rev. A 65 040302
[33]	Fiurášek J and Cerf N J 2008 Phys. Rev. A 77 052308
[34]	Kato G 2010 Phys. Rev. A 82 032314
[35]	Huang Y F, Li W L, Li C F, Zhang Y S, Jiang Y K and Guo G C 2001 Phys. Rev. A 64 012315
[36]	Sciarrino F, Sias C, Ricci M and Martini F D 2004 Phys. Rev. A 70 052305
[37]	Sciarrino F and Martini F D 2005 Phys. Rev. A 72 062313
[38]	Čeernoch A, Bartůšková L, Soubusta J, Jezěk M, Fiurásěk J and Dusěk M 2006 Phys. Rev. A 74 042327
[39]	Nagali E, Angelis T D, Sciarrino F and Martini F D 2007 Phys. Rev. A 76 042126
[40]	Bartůšková L, Dusěk M, Černoch A, Soubusta J and Fiurásěk J 2007 Phys. Rev. Lett. 99 120505
[41]	Araneda G, Cisternas N, Jiménez O and Delgado A 2012 Phys. Rev. A 86 052332
[42]	Soubusta J, Bartůšková L, Černoch A, Dušuk M and Fiurásěk J 2008 Phys. Rev. A 78 052323
[43]	Cerf N J and Iblisdir S 2001 Phys. Rev. Lett. 87 247903
[44]	Fiurášek J, Cerf N J and Polzik E S 2004 Phys. Rev. Lett. 93 180501
[45]	Alexanian M 2006 Phys. Rev. A 73 045801
[46]	Sacchi M F 2007 Phys. Rev. A 75 042328
[47]	Fiurášek J and Cerf N J 2007 Phys. Rev. A 75 052335
[48]	Dong Y, Zou X, Li S and Guo G C 2007 Phys. Rev. A 76 014303
[49]	Braunstein S L, Cerf N J, Iblisdir S, van Loock P and Massar S 2001 Phys. Rev. Lett. 86 4938
[50]	Fiurášek J 2001 Phys. Rev. Lett. 86 4942
[51]	Sabuncu M, Andersen U L and Leuchs G 2007 Phys. Rev. Lett. 98 170503
[52]	Sabuncu M, Leuchs G and Andersen U L 2008 Phys. Rev. A 78 052312
[53]	Fan H, Matsumoto K and Wadati M 2001 Phys. Rev. A 64 064301
[54]	Iblisdir S, Acín A, Cerf N J, Filip R, Fiurášek J and Gisin N 2005 Phys. Rev. A 72 042328
[55]	Karimipour V and Rezakhani A T 2002 Phys. Rev. A 66 052111
[56]	Zhang W H and Ye L 2007 New J. Phys. 9 318
[57]	Zhang W H, Wu T, Ye L and Dai J L 2007 Phys. Rev. A 75 044303
[58]	Pati A K 1999 Phys. Rev. Lett. 83 2849
[59]	Zhang W H, Yu L B, Cao Z L and Ye L 2012 Phys. Rev. A 86 022322
[60]	Zou X, Pahlke K and Mathis W 2003 Phys. Rev. A 67 024304
[61]	Milman P, Ollivier H and Raimond J M 2003 Phys. Rev. A 67 012314
[62]	Zhang W H and Ye L 2006 Phys. Lett. A 353 130
[63]	Zhang W H and Ye L 2006 Phys. Lett. A 354 344
[64]	Zou X B, Dong Y L and Guo G C 2006 Phys. Lett. A 360 44
[65]	Zou X B and Mathis W 2005 Phys. Rev. A 72 024304
[66]	Zheng S B 2007 J. Phys. B 40 989
[67]	Zheng S B and Guo G C 2005 Phys. Rev. A 72 064303
[68]	Meng F, Zhu A D, Yeon K H and Yu S C 2009 J. Phys. B 42 165504
[69]	Zhu A D, Yeon K H and Yu S C 2009 J. Phys. B 42 235501
[70]	Meng F Y, Zhu A D, Yeon K H and Yu S C 2010 Phys. Scr. 81 015009
[71]	Zhang W H and Ye L 2006 Phys. Lett. A 353 130
[72]	Xiong W and Ye L 2011 J. Opt. Soc. Am. B 28 2260
[73]	Fang B L, Wu T and Ye L 2012 Quantum Inf. Comput. 12 334
[74]	Fang B L, Wu T and Ye L 2012 Europhys. Lett. 97 60002
[75]	Fang B L, Song Q M and Ye L 2011 Phys. Rev. A 83 042309
[76]	Yu T, Zhu A D and Zhang S 2012 Chin. Phys. B 21 050304
[77]	Zhou Y H, Wang L and Lai X L 2013 Chin. Phys. B 22 050305
[78]	Yu L B, Zhang W H and Ye L 2007 Phys. Rev. A 76 034303
[79]	Yu L B, Zhang W H and Ye L 2007 Phys. Lett. A 365 74
[80]	Yang J, Yu Y F, Zhang Z M and Liu S H 2008 Phys. Rev. A 77 034302
[81]	Fang B L, Yang Z and Ye L 2009 Phys. Rev. A 79 054308
[82]	Fang B L, Hu G Y and Ye L 2009 J. Phys. B 42 075501
[83]	Ye L, Jin L and Zhang W H 2009 J. Mod. Opt. 56 661
[84]	Fang B L and Ye L 2010 Phys. Lett. A 374 1966
[85]	Yang R C, Li H C, Lin X, Huang Z P, Xie H, Lin H F and Huang G R 2007 Opt. Commun. 279 399
[86]	Lu D M and Zheng S B 2008 Commun. Theor. Phys. 49 649
[87]	Yang R C, Li H C, Lin X, Huang Z P and Xie H 2008 Chin. Phys. B 17 967
[88]	Hu G Y, Wan H B and Ye L 2010 J. Opt. Soc. Am. B 27 328
[89]	Wu T, Fang B L and Ye L 2012 J. Opt. Soc. Am. B 29 2749
[90]	Simon C, Weihs G and Zeilinger A 2000 Phys. Rev. Lett. 84 2993
[91]	Martini F D, Buzek V, Sciarrino F and Sias C 2002 Nature 419 815
[92]	Fasel S, Gisin N, Ribordy G, Scarani V and Zbinden H 2002 Phys. Rev. Lett. 89 107901
[93]	Martini F D, Pelliccia D and Sciarrino F 2004 Phys. Rev. Lett. 92 067901
[94]	Ricci M, Sciarrino F, Sias C and Martini F D 2004 Phys. Rev. Lett. 92 047901
[95]	Irvine W T M, Linares A L, de Dood M J A and Bouwmeester D 2004 Phys. Rev. Lett. 92 047902
[96]	Ali Khan I and Howell J C 2004 Phys. Rev. A 70 010303
[97]	Zhao Z, Zhang A N, Zhou X Q, Chen Y A, Lu C Y, Karlsson A and Pan J W 2005 Phys. Rev. Lett. 95 030502
[98]	Bartůšková L, Dusěk M, Černoch A, Soubusta J and Fiurásěk J 2007 Phys. Rev. Lett. 99 120505
[99]	Lemr K, Bartkiewicz K and Černoch A 2012 Phys. Rev. A 85 050307
[100]	Xu J S, Li C F, Chen L, Zou X B and Guo G C 2008 Phys. Rev. A 78 032322
[101]	Nagali E, Giovannini D, Marrucci L, Slussarenko S, Santamato E and Sciarrino F 2010 Phys. Rev. Lett. 105 073602
[102]	Nagali E, Sansoni L, Sciarrino F, Martini F D, Marrucci L, Piccirillo B, Karimi E and Santamato E 2009 Nat. Photon. 3 720
[103]	Raeisi S, Tittel W and Simon C 2012 Phys. Rev. Lett. 108 120404
[104]	Zou X and Mathis W 2005 Phys. Rev. A 72 022306
[105]	Zou X, Li K and Guo G C 2007 Phys. Lett. A 366 36
[106]	Zhang W H and Ye L 2009 Opt.Commun. 282 2650
[107]	Hu G Y, Zhang W H and Ye L 2010 Opt. Commun. 283 200
[108]	Wan H B and Ye L 2010 Commun. Theor. Phys. 53 1087
[109]	Cummins H K, Jones C, Furze A, Soffe N F, Mosca M, Peach J M and Jones J A 2002 Phys. Rev. Lett. 88 187901
[110]	Jiang Z, Chen Q and Wan S L 2007 Phys. Rev. A 76 034302
[111]	Chen Y H, Shao X Q, Zhu A D, Yeon K H and Yu S C 2010 Phys. Rev. A 81 032338
[112]	Raimond J M, Brune M and Haroche S 2001 Rev. Mod. Phys. 73 565
[113]	Saffman M, Walker T G and Molmer K 2010 Rev. Mod. Phys. 82 2313
[114]	Duan L M and Monroe C 2010 Rev. Mod. Phys. 82 1209
[115]	Kok P, Munro W J, Nemoto K, Ralph T C, Dowling J P and Milburn G J 2007 Rev. Mod. Phys. 79 135
[116]	Černoch A, Bartůšková L, Soubusta J, Jezěk M, Fiurásěk J and Dusěk M 2006 Phys. Rev. A 74 042327
[117]	Lamas L A, Simon C, Howell J C and Bouwmeester D 2002 Science 296 712
[118]	Xiang G Y, Ralph T C, Lund A P, Walk N and Pryde G J 2010 Nat. Photon. 4 316
[119]	Du J, Durt T, Zou P, Li H, Kwek L C, Lai C H, Oh C H and Ekert A 2005 Phys. Rev. Lett. 94 040505
[120]	Chen H, Zhou X, Suter D and Du J 2007 Phys. Rev. A 75 012317
[121]	Chang Y C, Liu G Q, Liu D Q, Fan H and Pan X Y 2013 Sci. Rep. 3 1498

[1]	Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[2]	Implementation of an 8-bit bit-slice AES S-box with rapid single flux quantum circuits Ruo-Ting Yang(杨若婷), Xin-Yi Xue(薛新伊), Shu-Cheng Yang(杨树澄), Xiao-Ping Gao(高小平), Jie Ren(任洁), Wei Yan(严伟), and Zhen Wang(王镇). Chin. Phys. B, 2022, 31(9): 098501.
[3]	Exponential sine chaotification model for enhancing chaos and its hardware implementation Rui Wang(王蕊), Meng-Yang Li(李孟洋), and Hai-Jun Luo(罗海军). Chin. Phys. B, 2022, 31(8): 080508.
[4]	Analysis and implementation of new fractional-order multi-scroll hidden attractors Li Cui(崔力), Wen-Hui Luo(雒文辉), and Qing-Li Ou(欧青立). Chin. Phys. B, 2021, 30(2): 020501.
[5]	Heterogeneous dual memristive circuit: Multistability, symmetry, and FPGA implementation Yi-Zi Cheng(承亦梓), Fu-Hong Min(闵富红), Zhi Rui(芮智), and Lei Zhang(张雷). Chin. Phys. B, 2021, 30(12): 120502.
[6]	Transient transition behaviors of fractional-order simplest chaotic circuit with bi-stable locally-active memristor and its ARM-based implementation Zong-Li Yang(杨宗立), Dong Liang(梁栋), Da-Wei Ding(丁大为), Yong-Bing Hu(胡永兵), and Hao Li(李浩). Chin. Phys. B, 2021, 30(12): 120515.
[7]	Novel two-directional grid multi-scroll chaotic attractors based on the Jerk system Peng-Fei Ding(丁鹏飞), Xiao-Yi Feng(冯晓毅)†, and Cheng-Mao Wu(吴成茂). Chin. Phys. B, 2020, 29(10): 108202.
[8]	Probabilistic direct counterfactual quantum communication Sheng Zhang(张盛). Chin. Phys. B, 2017, 26(2): 020304.
[9]	A novel methodology for constructing a multi-wing chaotic and hyperchaotic system with a unified step function switching control Chao-Xia Zhang(张朝霞), Si-Min Yu(禹思敏). Chin. Phys. B, 2016, 25(5): 050503.
[10]	Study on a new chaotic bitwise dynamical system and its FPGA implementation Wang Qian-Xue (王倩雪), Yu Si-Min (禹思敏), C. Guyeux, J. Bahi, Fang Xiao-Le (方晓乐). Chin. Phys. B, 2015, 24(6): 060503.
[11]	Scheme for purifying a general mixed entangled state and its linear optical implementation Dong Dong (董冬), Zhang Yan-Lei (张延磊), Zou Chang-Ling (邹长铃), Zou Xu-Bo (邹旭波), Guo Guang-Can (郭光灿). Chin. Phys. B, 2015, 24(10): 100306.
[12]	Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system Xue Wei (薛薇), Qi Guo-Yuan (齐国元), Mu Jing-Jing (沐晶晶), Jia Hong-Yan (贾红艳), Guo Yan-Ling (郭彦岭). Chin. Phys. B, 2013, 22(8): 080504.
[13]	Scheme for implementing economical phase-covariant quantum cloning machine of distant atomic qubits with single-photon interference Zhou Yan-Hui (周彦辉), Wang Lei (王磊), Lai Xiao-Lei (赖晓磊). Chin. Phys. B, 2013, 22(5): 050305.
[14]	Controlled remote implementation of quantum operations with high-dimensional systems Zhan You-Bang (詹佑邦), Li Xiao-Wei (李晓薇), Ma Peng-Cheng (马鹏程), Shi Jin (施锦). Chin. Phys. B, 2013, 22(4): 040306.
[15]	Forming and implementing a hyperchaotic system with rich dynamics Liu Wen-Bo(刘文波), Wallace K. S. Tang(邓榤生), and Chen Guan-Rong(陈关荣) . Chin. Phys. B, 2011, 20(9): 090510.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Quantum cloning machines and their implementation in physical systems

Cite this article:

Online attention