Hyper-parallel photonic quantum computation and manipulation on hyperentangled states

Ren Bao-Cang; Deng Fu-Guo

doi:10.7498/aps.64.160303

Abstract

Photon system is a promising candidate for quantum information processing, and it can be used to achieve some important tasks with the interaction between a photon and an atom (or a artificial atom), such as the transmission of secret information, the storage of quantum states, and parallel quantum computing. Several degrees of freedom (DOFs) of a photon system can be used to carry information in the realization of quantum information processing, such as the polarization, spatial-mode, orbit-angular-momentum, time-bin, and frequency DOFs. A hyperparallel quantum computer can implement the quantum operations on several DOFs of a quantum system simultaneously, which reduces the operation time and the resources consumed in quantum information processing. The hyperparallel quantum operations are more robust against the photonic dissipation noise than the quantum computing in one DOF of a photon system. Hyperentanglement, defined as the entanglement in several DOFs of a quantum system, can improve the channel capacity and the security of long-distance quantum communication, and it can also be conductive to completing some important tasks in quantum communication. Hyperentangled Bell-state analysis is used to completely distinguish the 16 hyperentangled Bell states, which is very useful in high-capacity quantum communication protocols and quantum repeaters. In order to depress the effect of noises in quantum channel, hyperentanglement concentration and hyperentanglement purification are required to improve the entanglement of the quantum systems in long-distance quantum communication, which is also very useful in high-capacity quantum repeaters. Hyperentanglement concentration is used to distill several nonlocal photon systems in a maximally hyperentangled state from those in a partially hyperentangled pure state, and hyperentanglement purification is used to distill several nonlocal photon systems in a high-fidelity hyperentangled state from those in a mixed hyperentangled state with less entanglement. In this reviewing article, we review some new applications of photon systems with multiple DOFs in quantum information processing, including hyperparallel photonic quantum computation, hyperentangled-Bell-state analysis, hyperentanglement concentration, and hyperentanglement purification.

Keywords:

Authors and contacts

1.
Department of Physics, Beijing Normal University, Beijing 100875, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11474026).

References

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[58]	Li X H, Deng F G, Zhou H Y 2008 Phys. Rev. A 78 022321
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[61]	Xiao L, Long G L, Deng F G, Pan J W 2004 Phys. Rev. A 69 052307
[62]	Long G L, Liu X S 2002 Phys. Rev. A 65 032302
[63]	Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68 042317
[64]	Deng F G, Long G L 2004 Phys. Rev. A 69 052319
[65]	Wang C, Deng F G, Li Y S, Liu X S, Long G L 2005 Phys. Rev. A 71 044305
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[67]	Dür W, Briegel H J, Cirac J I, Zoller P 1999 Phys. Rev. A 59 169
[68]	Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413
[69]	Matsukevich D N, Kuzmich A 2004 Science 306 663
[70]	Chou C W, de Riedmatten H, Felinto D, Polyakov S V, van Enk S J, Kimble H J 2005 Nature 438 828
[71]	Chou C W, Laurat J, Deng H, Choi K S, de Riedmatten H, Felinto D, Kimble H J 2007 Science 316 1316
[72]	Chen S, Chen Y A, Zhao B, Yuan Z S, Schmiedmayer J, Pan J W 2007 Phys. Rev. Lett. 99 180505
[73]	Wang T J, Song S Y, Long G L 2012 Phys. Rev. A 85 062311
[74]	Hu C Y, Young A, O'Brien J L, Munro W J, Rarity J G 2008 Phys. Rev. B 78 085307
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[76]	Zhao Z, Pan J W, Zhan M S 2001 Phys. Rev. A 64 014301
[77]	Yamamoto T, Koashi M, Imoto N 2001 Phys. Rev. A 64 012304
[78]	Sheng Y B, Deng F G, Zhou H Y 2008 Phys. Rev. A 77 062325
[79]	Sheng Y B, Zhou L 2013 Entropy 15 1776
[80]	Wang C, Zhang Y, Jin G S 2011 Phys. Rev. A 84 032307
[81]	Wang C 2012 Phys. Rev. A 86 012323
[82]	Bose S, Vderal V, Knight P L 1999 Phys. Rev. A 60 194
[83]	Shi B S, Jiang Y K, Guo G C 2000 Phys. Rev. A 62 054301
[84]	Sheng Y B, Zhou L, Zhao S M, Zheng B Y 2012 Phys. Rev. A 85 012307
[85]	Deng F G 2012 Phys. Rev. A 85 022311
[86]	Sheng Y B, Zhou L, Zhao S M 2012 Phys. Rev. A 85 042302
[87]	Zhang W Z, Li W D, Shi P, Gu Y J 2011 Acta Phys. Sin. 60 060303 (in Chinese) [张闻钊, 李文东, 史鹏, 顾永建 2011 物理学报 60 060303]
[88]	Du F F, Deng F G
[89]	Maimaiti W, Li Z, Chesi S, et al.
[90]	Zhang R, Zhou S H, Cao C 2014 Sci. China: Phys. Mech. Astron. 57 1511
[91]	Sheng Y B, Liu J, Zhao S Y, et al. 2013 Chin. Sci. Bull. 58 3507
[92]	Wang C, He L Y, Zhang Y, et al. 2013 Sci. China: Phys. Mech. Astron. 56 2054
[93]	Bennett C H, Brassard G, Popescu S, Schumacher B, Smolin J A, Wootters W K 1996 Phys. Rev. Lett. 76 722
[94]	Pan J W, Simon C, Brukner C, Zellinger A 2001 Nature 410 1067
[95]	Simon C, Pan J W 2002 Phys. Rev. Lett. 89 257901
[96]	Sheng Y B, Deng F G, Zhou H Y 2008 Phys. Rev. A 77 042308
[97]	Sheng Y B, Deng F G 2010 Phys. Rev. A 81 032307
[98]	Sheng Y B, Deng F G 2010 Phys. Rev. A 82 044305
[99]	Li X H 2010 Phys. Rev. A 82 044304
[100]	Deng F G 2011 Phys. Rev. A 83 062316
[101]	Sheng Y B, Zhou L 2014 Laser Phys. Lett. 11 085203
[102]	Li T, Yang G J, Deng F G 2014 Opt. Express 22 23897
[103]	Liu Y 2013 Chin. Sci. Bull. 58 2927
[104]	Ding D, Yan F L 2013 Acta Phys. Sin. 62 100304
[105]	Ding D, Yan F L 2013 Acta Phys. Sin. 62 010302 (in Chinese) [丁东, 闫凤利 2013 物理学报 62 010302]

Cited By

[1]	Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) pp1-59
[2]	Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145
[3]	Kok P, Munro W J, Nemoto K, Ralph T C, Dowling J P, Milburn G J 2007 Rev. Mod. Phys. 79 135
[4]	Yoran N, Reznik B 2003 Phys. Rev. Lett. 91 037903
[5]	Zhang P, Liu R F, Huang Y F, Gao H, Li F L 2010 Phys. Rev. A 82 064302
[6]	Ren B C, Wei H R, Deng F G 2013 Laser Phys. Lett. 10 095202
[7]	Ren B C, Deng F G
[8]	Ren B C, Wang G Y, Deng F G 2015 Phys. Rev. A 91 032328
[9]	Kwiat P G 1997 J. Mod. Opt. 44 2173
[10]	Sheng Y B, Deng F G, Long G L 2010 Phys. Rev. A 82 032318
[11]	Ren B C, Wei H R, Hua M, Li T, Deng F G 2012 Opt. Express 20 24664
[12]	Wang T J, Lu Y, Long G L 2012 Phys. Rev. A 86 042337
[13]	Ren B C, Du F F, Deng F G 2013 Phys. Rev. A 88 012302
[14]	Ren B C, Du F F, Deng F G 2014 Phys. Rev. A 90 052309
[15]	Ren B C, Deng F G 2013 Laser Phys. Lett. 10 115201
[16]	Ren B C, Long G L 2014 Opt. Express 22 6547
[17]	Li X H, Ghose S 2014 Laser Phys. Lett. 11 125201
[18]	Li X H, Ghose S 2015 Opt. Express 23 3550
[19]	Wang T J, Cao C, Wang C 2014 Phys. Rev. A 89 052303
[20]	Wang T J, Zhang Y, Wang C 2014 Laser Phys. Lett. 11 025203
[21]	Luo M X, Chen X B, Yang Y X, Qu Z G, Wang X J
[22]	Liu Q, Zhang M 2013 J. Opt. Soc. Am. B 30 2263
[23]	Yan X, Yu Y F, Zhang Z M 2014 Chin. Phys. B 23 060306
[24]	Ji Y Q, Jin Z, Zhu A D, Wang H F, Zhang S 2014 Chin. Phys. B 23 050306
[25]	Hong C H, Heoa J, Lima J I, Yang H J 2014 Chin. Phys. B 23 090309
[26]	Fan L L, Xia Y, Song J 2014 Quantum Inf. Process 13 1967
[27]	Chen X, Zeng Z, Li X H 2014 Commun. Theor. Phys. 61 322
[28]	Wang X L, Cai X D, Su Z E, et al. 2015 Nature 518 516
[29]	Knill E, Laflamme R, Milburn G J 2001 Nature 409 46
[30]	O'Brien J L, Pryde G J, White A G, Ralph T C, Branning D 2003 Nature 426 264
[31]	Duan L M, Kimble H J 2004 Phys. Rev. Lett. 92 127902
[32]	Menicucci N C, Flammia S T, Pfister O 2008 Phys. Rev. Lett. 101 130501
[33]	Langford N K, Ramelow S, Prevedel R, et al. 2011 Nature 478 360
[34]	Wei H R, Deng F G 2013 Opt. Express 21 17671
[35]	Hua M, Tao M J, Deng F G 2014 Phys. Rev. A 90 012328
[36]	Hua M, Tao M J, Deng F G 2015 Sci. Rep. 5 9274
[37]	Li X Q, Wu Y W, Steel D, et al. 2003 Science 301 809
[38]	Beenakker C W J, DiVincenzo D P, Emary C, Kindermann M 2004 Phys. Rev. Lett. 93 020501
[39]	Xu G F, Zhang J, Tong D M, Sjöqvist E, Kwek L C 2012 Phys. Rev. Lett. 109 170501
[40]	Wei H R, Deng F G 2013 Phys. Rev. A 88 042323
[41]	Wei H R, Deng F G 2014 Sci. Rep. 4 7551
[42]	Gershenfeld N A, Chuang I L 1997 Science 275 350
[43]	Jones J A, Mosca M, Hansen R H 1998 Nature 393 344
[44]	Feng G R, Xu G F, Long G L 2013 Phys. Rev. Lett. 110 190501
[45]	Long G L, Xiao L 2004 Phys. Rev. A 69 052303
[46]	Long G L, Xiao L 2003 J. Chem. Phys. 119 8473
[47]	Turchette Q A, Hood C J, Lange W, Mabuchi H, Kimble H J 1995 Phys. Rev. Lett. 75 4710
[48]	Rauschenbeutel A, Nogues G, Osnaghi S, et al. 1999 Phys. Rev. Lett. 83 5166
[49]	Yamamoto T, Pashkin Y A, Astafiev O, Nakamura Y, Tsai J S 2003 Nature 425 941
[50]	Blais A, Huang R S, Wallraff A, Girvin S M, Schoelkopf R J 2004 Phys. Rev. A 69 062320
[51]	Wallraff A, Schuster D I, Blais A, et al. 2004 Nature 431 162
[52]	DiCarlo L, Chow J M, Gambetta J M, et al. 2009 Nature 460 240
[53]	Schmidt-Kaler F, Höffner H, Riebe M, et al. 2003 Nature 422 408
[54]	Hu C Y, Munro W J, O'Brien J L, Rarity J G 2009 Phys. Rev. B 80 205326
[55]	Bennett C H, Brassard G 1984 Proceedings of IEEE International Conference on Computers, Systems and Signal Processing Bangalore, India, IEEE, New York 1984 p175
[56]	Ekert A K 1991 Phys. Rev. Lett. 67 661
[57]	Bennett C H, Brassard G, Mermin N D 1992 Phys. Rev. Lett. 68 557
[58]	Li X H, Deng F G, Zhou H Y 2008 Phys. Rev. A 78 022321
[59]	Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1829
[60]	Karlsson A, Koashi M, Imoto N 1999 Phys. Rev. A 59 162
[61]	Xiao L, Long G L, Deng F G, Pan J W 2004 Phys. Rev. A 69 052307
[62]	Long G L, Liu X S 2002 Phys. Rev. A 65 032302
[63]	Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68 042317
[64]	Deng F G, Long G L 2004 Phys. Rev. A 69 052319
[65]	Wang C, Deng F G, Li Y S, Liu X S, Long G L 2005 Phys. Rev. A 71 044305
[66]	Briegel H J, Dür W, Cirac J I, Zoller P 1998 Phys. Rev. Lett. 81 5932
[67]	Dür W, Briegel H J, Cirac J I, Zoller P 1999 Phys. Rev. A 59 169
[68]	Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413
[69]	Matsukevich D N, Kuzmich A 2004 Science 306 663
[70]	Chou C W, de Riedmatten H, Felinto D, Polyakov S V, van Enk S J, Kimble H J 2005 Nature 438 828
[71]	Chou C W, Laurat J, Deng H, Choi K S, de Riedmatten H, Felinto D, Kimble H J 2007 Science 316 1316
[72]	Chen S, Chen Y A, Zhao B, Yuan Z S, Schmiedmayer J, Pan J W 2007 Phys. Rev. Lett. 99 180505
[73]	Wang T J, Song S Y, Long G L 2012 Phys. Rev. A 85 062311
[74]	Hu C Y, Young A, O'Brien J L, Munro W J, Rarity J G 2008 Phys. Rev. B 78 085307
[75]	Bennett C H, Bernstein H J, Popescu S, Schumacher B 1996 Phys. Rev. A 53 2046
[76]	Zhao Z, Pan J W, Zhan M S 2001 Phys. Rev. A 64 014301
[77]	Yamamoto T, Koashi M, Imoto N 2001 Phys. Rev. A 64 012304
[78]	Sheng Y B, Deng F G, Zhou H Y 2008 Phys. Rev. A 77 062325
[79]	Sheng Y B, Zhou L 2013 Entropy 15 1776
[80]	Wang C, Zhang Y, Jin G S 2011 Phys. Rev. A 84 032307
[81]	Wang C 2012 Phys. Rev. A 86 012323
[82]	Bose S, Vderal V, Knight P L 1999 Phys. Rev. A 60 194
[83]	Shi B S, Jiang Y K, Guo G C 2000 Phys. Rev. A 62 054301
[84]	Sheng Y B, Zhou L, Zhao S M, Zheng B Y 2012 Phys. Rev. A 85 012307
[85]	Deng F G 2012 Phys. Rev. A 85 022311
[86]	Sheng Y B, Zhou L, Zhao S M 2012 Phys. Rev. A 85 042302
[87]	Zhang W Z, Li W D, Shi P, Gu Y J 2011 Acta Phys. Sin. 60 060303 (in Chinese) [张闻钊, 李文东, 史鹏, 顾永建 2011 物理学报 60 060303]
[88]	Du F F, Deng F G
[89]	Maimaiti W, Li Z, Chesi S, et al.
[90]	Zhang R, Zhou S H, Cao C 2014 Sci. China: Phys. Mech. Astron. 57 1511
[91]	Sheng Y B, Liu J, Zhao S Y, et al. 2013 Chin. Sci. Bull. 58 3507
[92]	Wang C, He L Y, Zhang Y, et al. 2013 Sci. China: Phys. Mech. Astron. 56 2054
[93]	Bennett C H, Brassard G, Popescu S, Schumacher B, Smolin J A, Wootters W K 1996 Phys. Rev. Lett. 76 722
[94]	Pan J W, Simon C, Brukner C, Zellinger A 2001 Nature 410 1067
[95]	Simon C, Pan J W 2002 Phys. Rev. Lett. 89 257901
[96]	Sheng Y B, Deng F G, Zhou H Y 2008 Phys. Rev. A 77 042308
[97]	Sheng Y B, Deng F G 2010 Phys. Rev. A 81 032307
[98]	Sheng Y B, Deng F G 2010 Phys. Rev. A 82 044305
[99]	Li X H 2010 Phys. Rev. A 82 044304
[100]	Deng F G 2011 Phys. Rev. A 83 062316
[101]	Sheng Y B, Zhou L 2014 Laser Phys. Lett. 11 085203
[102]	Li T, Yang G J, Deng F G 2014 Opt. Express 22 23897
[103]	Liu Y 2013 Chin. Sci. Bull. 58 2927
[104]	Ding D, Yan F L 2013 Acta Phys. Sin. 62 100304
[105]	Ding D, Yan F L 2013 Acta Phys. Sin. 62 010302 (in Chinese) [丁东, 闫凤利 2013 物理学报 62 010302]

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