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A generation algorithm of unitary transformation applied in quantum data compression

Liang Yan-Xia Nie Min

A generation algorithm of unitary transformation applied in quantum data compression

Liang Yan-Xia, Nie Min
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  • An algorithm to generate unitary transformation (UT) of two orthogonal base kets is proposed in this paper. Certain requirements that UT must meet are as follows: four typical base kets in the first category can be transformed into states with the last qubit |0>, and the other four atypical base kets can be transformed into states with the last qubit |1>. This UT is applied to quantum data compression, with a result that the fidelity of the compression is 0.942. This method provides an important basis for realizing quantum compression and decompression. And it can be an important reference of other UT generation method which must fulfill some requirements.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61172071, 61102047), the National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2012ZX03001025-004 ), and the Special Scientific Research Fundation of the Education Department of Shaanxi Province, China (Grant No. 11JK1016).
    [1]

    Li S, Ma H Q, Wu L A, Zhai G J 2013 Acta Phys. Sin. 62 084214 (in Chinese) [李申, 马海强, 吴令安, 翟光杰 2013 物理学报 62 084214]

    [2]

    Zhou N R, Zeng B Y, Wang L J, Gong L H 2010 Acta Phys. Sin. 59 2193 (in Chinese) [周南润, 曾宾阳, 王立军, 龚黎华 2010 物理学报 59 2193]

    [3]

    Zhou N R, Zeng G H, Gong L H, Liu S Q 2007 Acta Phys. Sin. 56 5066 (in Chinese) [周南润, 曾贵华, 龚黎华, 刘三秋 2007 物理学报 56 5066]

    [4]

    Sheng Y B, Zhou L, Cheng W W, Gong L Y, Zhao S M, Zheng B Y 2012 Chin. Phys. B 21 030307

    [5]

    Zhang C L, Wang C, Cao C, Zhang R 2012 Chin. Phys. Lett. 29 070305

    [6]

    Yu X T, Xu J, Zhang Z C 2012 Acta Phys. Sin. 61 220303 (in Chinese) [余旭涛, 徐进, 张在琛 2012 物理学报 61 220303]

    [7]

    Zhou X Q, Wu Y W 2012 Acta Phys. Sin. 61 170303 (in Chinese) [周小清, 邬云文 2012 物理学报 61 170303]

    [8]

    Zhou X Q, Wu Y W, Zhao H 2011 Acta Phys. Sin. 60 040304 (in Chinese) [周小清, 邬云文, 赵晗 2011 物理学报 60 040304]

    [9]

    Wang M Y, Yan F L 2011 Chin. Phys. B 20 120309

    [10]

    Guo Yu, Luo X B 2012 Chin. Phys. Lett. 29 060303

    [11]

    Zhu W, Nie M 2013 Acta Phys. Sin. 62 130304 (in Chinese) [朱伟, 聂敏 2013 物理学报 62 130304]

    [12]

    Schumacher B 1995 Phys. Rev. A 51 2738

    [13]

    Cleve R, Divicenzo D 1996 Phys. Rev. A 54 2636

    [14]

    Jozsa R, Horodecki M, Horodecki P, Horodecki R 1998 Phys. Rev. Lett. 81 1714

    [15]

    Ahn C, Doherty A C, Hayden P, Winter A J 2006 IEEE Trans. Inform. Theory 52 4349

    [16]

    Avis D, Hayden P, Savov I 2008 Proceedings of 2008 Sencond International Conference on Quantum Nano and Micro Technologies Sainte Luce, Martinique, February 10-15, 2008 p90

    [17]

    Hayashi M 2002 Phys. Rev. A 66 032321

    [18]

    Hayashi M, Matsumoto K 2002 Phys. Rev. A 66 022311

    [19]

    Chuang I L, Modha D S 2000 IEEE Trans. Inform. Theory 46 1104

    [20]

    Desuvire E 2009 Classical and Quantum Information Theory (New York: Cambridge University Press) p457

  • [1]

    Li S, Ma H Q, Wu L A, Zhai G J 2013 Acta Phys. Sin. 62 084214 (in Chinese) [李申, 马海强, 吴令安, 翟光杰 2013 物理学报 62 084214]

    [2]

    Zhou N R, Zeng B Y, Wang L J, Gong L H 2010 Acta Phys. Sin. 59 2193 (in Chinese) [周南润, 曾宾阳, 王立军, 龚黎华 2010 物理学报 59 2193]

    [3]

    Zhou N R, Zeng G H, Gong L H, Liu S Q 2007 Acta Phys. Sin. 56 5066 (in Chinese) [周南润, 曾贵华, 龚黎华, 刘三秋 2007 物理学报 56 5066]

    [4]

    Sheng Y B, Zhou L, Cheng W W, Gong L Y, Zhao S M, Zheng B Y 2012 Chin. Phys. B 21 030307

    [5]

    Zhang C L, Wang C, Cao C, Zhang R 2012 Chin. Phys. Lett. 29 070305

    [6]

    Yu X T, Xu J, Zhang Z C 2012 Acta Phys. Sin. 61 220303 (in Chinese) [余旭涛, 徐进, 张在琛 2012 物理学报 61 220303]

    [7]

    Zhou X Q, Wu Y W 2012 Acta Phys. Sin. 61 170303 (in Chinese) [周小清, 邬云文 2012 物理学报 61 170303]

    [8]

    Zhou X Q, Wu Y W, Zhao H 2011 Acta Phys. Sin. 60 040304 (in Chinese) [周小清, 邬云文, 赵晗 2011 物理学报 60 040304]

    [9]

    Wang M Y, Yan F L 2011 Chin. Phys. B 20 120309

    [10]

    Guo Yu, Luo X B 2012 Chin. Phys. Lett. 29 060303

    [11]

    Zhu W, Nie M 2013 Acta Phys. Sin. 62 130304 (in Chinese) [朱伟, 聂敏 2013 物理学报 62 130304]

    [12]

    Schumacher B 1995 Phys. Rev. A 51 2738

    [13]

    Cleve R, Divicenzo D 1996 Phys. Rev. A 54 2636

    [14]

    Jozsa R, Horodecki M, Horodecki P, Horodecki R 1998 Phys. Rev. Lett. 81 1714

    [15]

    Ahn C, Doherty A C, Hayden P, Winter A J 2006 IEEE Trans. Inform. Theory 52 4349

    [16]

    Avis D, Hayden P, Savov I 2008 Proceedings of 2008 Sencond International Conference on Quantum Nano and Micro Technologies Sainte Luce, Martinique, February 10-15, 2008 p90

    [17]

    Hayashi M 2002 Phys. Rev. A 66 032321

    [18]

    Hayashi M, Matsumoto K 2002 Phys. Rev. A 66 022311

    [19]

    Chuang I L, Modha D S 2000 IEEE Trans. Inform. Theory 46 1104

    [20]

    Desuvire E 2009 Classical and Quantum Information Theory (New York: Cambridge University Press) p457

  • [1] Long Chao-Yun. The quantum fluctuation of parallel mesoscopic RLC circuit. Acta Physica Sinica, 2003, 52(8): 2033-2036. doi: 10.7498/aps.52.2033
    [2] Shi Shen-Lei, Shen Jian-Qi, Zhu Hong-Yi. . Acta Physica Sinica, 2002, 51(3): 536-540. doi: 10.7498/aps.51.536
    [3] Shi Qing-Fan, Li Liang-Sheng, Zhang Mei. Effectivity of Hamiltonian terms of "forbidden" 3-magnon interaction. Acta Physica Sinica, 2004, 53(11): 3916-3919. doi: 10.7498/aps.53.3916
    [4] FU JIAN, GAO XIAO-CHUN, XU JING-BO, ZOU XU-BO. INVARIANT-RELATED UNITARY TRANSFORMATION METHOD AND EXACT SOLUTIONS FOR THE QUANTUM DIRAC FIELD IN A TIME-DEPENDENT SPATIALLY HOMOGENEOUS ELECTRIC FIELD. Acta Physica Sinica, 1999, 48(6): 1011-1022. doi: 10.7498/aps.48.1011
    [5] Zha Xin-Wei. The expansion of orthogonal complete set and transformation operator in teleportation. Acta Physica Sinica, 2007, 56(4): 1875-1880. doi: 10.7498/aps.56.1875
    [6] . Acta Physica Sinica, 1975, 146(6): 438-447. doi: 10.7498/aps.24.438
    [7] HUO YU-PING, YANG GUO-ZHEN, GU BEN-YUAN. UNITARY TRANSFORMATION AND GENERAL LINEAR TRANSFORMATION BY AN OPTICAL METHOD (Ⅱ)——THE ITERATIVE METHOD OF SOLUTION. Acta Physica Sinica, 1976, 147(1): 31-46. doi: 10.7498/aps.25.31
    [8] Liang Xiu-Dong, Tai Yun-Jiao, Cheng Jian-Min, Zhai Long-Hua, Xu Ye-Jun. Transform relations between squeezed coherent state representation and quantum phase space distribution functions. Acta Physica Sinica, 2015, 64(2): 024207. doi: 10.7498/aps.64.024207
    [9] Sun Hong-Xiang, Chen Xiu-Bo, Shangguan Li-Ying, Wen Qiao-Yan, Zhu Fu-Chen. The expansion of orthogonal complete set and transformation operator in the teleportation of a three-particle entangled W state. Acta Physica Sinica, 2009, 58(3): 1371-1376. doi: 10.7498/aps.58.1371
    [10] Hu Ming-Liang, Xi Xiao-Qiang. A new method of calculating the unitary evolution matrix ds(t) of the spin-s operators and its applications. Acta Physica Sinica, 2008, 57(6): 3319-3323. doi: 10.7498/aps.57.3319
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  • Received Date:  05 June 2013
  • Accepted Date:  15 July 2013
  • Published Online:  20 October 2013

A generation algorithm of unitary transformation applied in quantum data compression

  • 1. School of Telecommunication and Information Engineering, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 61172071, 61102047), the National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2012ZX03001025-004 ), and the Special Scientific Research Fundation of the Education Department of Shaanxi Province, China (Grant No. 11JK1016).

Abstract: An algorithm to generate unitary transformation (UT) of two orthogonal base kets is proposed in this paper. Certain requirements that UT must meet are as follows: four typical base kets in the first category can be transformed into states with the last qubit |0>, and the other four atypical base kets can be transformed into states with the last qubit |1>. This UT is applied to quantum data compression, with a result that the fidelity of the compression is 0.942. This method provides an important basis for realizing quantum compression and decompression. And it can be an important reference of other UT generation method which must fulfill some requirements.

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