A generation algorithm of unitary transformation applied in quantum data compression
Liang Yan-Xia, Min Nie · Acta Physica Sinica · 2013
摘要 提出了一种两类正交基矢按照特定要求相互转换的幺正变换生成方法. 特定要求为第一类基矢中特定的四种典型基矢经幺正变换后, 第三个量子比特特定为|0>, 而四种非典型基矢经幺正变换后, 第三个量子比特为|1>. 将该幺正变换应用于量子数据压缩, 准确度达到0.942. 该方法的提出为量子压缩和解压缩的实现提供了基础, 对于其他要求特定对应关系的幺正变换的生成具有借鉴意义. 关键词: 幺正变换 / 正交基矢 / 特定要求 / 量子压缩 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. Keywords: unitary transformation / orthogonal base ket / certain requirement / quantum compression 作者及机构信息 梁彦霞, 聂敏 1. 西安邮电大学通信与信息工程学院, 西安 710121 基金项目: 国家自然科学基金(批准号: 61172071, 61102047)、国家科技重大专项(批准号: 2012ZX03001025-004)和陕西省教育厅科研计划专项(批准号: 11JK1016)资助的课题. Authors and contacts Liang Yan-Xia, Nie Min 1. School of Telecommunication and Information Engineering, Xi’an University of Posts and Telecommunications, Xi’an 710121, China 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). 参考文献 [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 施引文献