控制概率隐形传态及其量子线路和群组中实现的量子零知识证明
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摘要
量子信息学是量子力学、信息科学及计算机科学相结合而形成的一门新兴交叉学科。量子信息将为信息科学的发展开辟新的道路,同时它也极大地推动量子力学理论的发展。
量子纠缠是量子理论中一种奇特的现象,量子纠缠态是量子理论中最重要的一类量子态。量子纠缠也是量子信息与经典信息有根本区别的主要原因。
量子隐形传态是量子通信中进展最显著的方向之一,近年来己经在理论上和实验上取得重大的突破。本文归纳了包括量子隐形传态在内的几种常见的量子技术:量子稠密编码、量子隐形传态、量子纠缠交换、量子密码、量子秘密共享、量子安全直接通讯、量子认证、量子零知识证明。
而后我们根据量子隐形传态的基本原理,提出了一种利用三粒子纯态作为量子通道,传输未知单粒子态的概率隐形传输方案。选择的量子通道是特殊纠缠和非最大纠缠两种情形。并给出了实现传输过程的两种量子线路。
零知识证明是密码学中的一个基本方法。其优点是在证明了自己身份的同时,还确保了有用信息不泄露,有效防止了他人冒充。根据经典零知识证明的基本思想,以及量子安全通信方法,我们又设计了一种在群组中实现的量子零知识证明方案。
Quantum information is a new subject that is a combination of quantum mechanics, information science and computer science. Quantum information will inaugurate a new way for the developme- nt of information science. In addition, it is helpful for the research on basic problems of quantum mechanics itself.
Among various kinds of quantum states, the quantum-entangled state is the most important one in quantum information science. Entanglement is also the main reason that yields the essential difference between quantum information and classic information.
Being one of the directions of quantum communication, quantum teleportation makes great progress. In recent years, it has obtained important breakthrough in both theories and experiments. In this text we introduced a few familiar quantum techniques, such as quantum superdense coding, quantum teleportation, quantum swap- ping, quantum cryptology, quantum secret sharing, quantum secure direct communication, quantum identity authentication, quantum zero knowledge protocol and so on.
Further, we present simplification scheme for probabilistic and controlled teleportation of the unknown one-particle quantum state using the pure three-particle entangled state as the quantum chan- nel. Both special entangled state and non-maximum entangled state are used as quantum channels in the scheme. In addition, we also construct two efficient quantum logic networks for implementing the new scheme by means of the primitive operations.
Zero knowledge protocol is a basic method of cryptography. Its advantage is to keep others from pretending to be at the time of proving oneself, also to assure an useful information not to reveal. According to the basic thought of classical zero knowledge protoc- ol, we present a scheme for quantum zero knowledge protocol in group using a mode of quantum secure communication.
量子纠缠是量子理论中一种奇特的现象,量子纠缠态是量子理论中最重要的一类量子态。量子纠缠也是量子信息与经典信息有根本区别的主要原因。
量子隐形传态是量子通信中进展最显著的方向之一,近年来己经在理论上和实验上取得重大的突破。本文归纳了包括量子隐形传态在内的几种常见的量子技术:量子稠密编码、量子隐形传态、量子纠缠交换、量子密码、量子秘密共享、量子安全直接通讯、量子认证、量子零知识证明。
而后我们根据量子隐形传态的基本原理,提出了一种利用三粒子纯态作为量子通道,传输未知单粒子态的概率隐形传输方案。选择的量子通道是特殊纠缠和非最大纠缠两种情形。并给出了实现传输过程的两种量子线路。
零知识证明是密码学中的一个基本方法。其优点是在证明了自己身份的同时,还确保了有用信息不泄露,有效防止了他人冒充。根据经典零知识证明的基本思想,以及量子安全通信方法,我们又设计了一种在群组中实现的量子零知识证明方案。
Quantum information is a new subject that is a combination of quantum mechanics, information science and computer science. Quantum information will inaugurate a new way for the developme- nt of information science. In addition, it is helpful for the research on basic problems of quantum mechanics itself.
Among various kinds of quantum states, the quantum-entangled state is the most important one in quantum information science. Entanglement is also the main reason that yields the essential difference between quantum information and classic information.
Being one of the directions of quantum communication, quantum teleportation makes great progress. In recent years, it has obtained important breakthrough in both theories and experiments. In this text we introduced a few familiar quantum techniques, such as quantum superdense coding, quantum teleportation, quantum swap- ping, quantum cryptology, quantum secret sharing, quantum secure direct communication, quantum identity authentication, quantum zero knowledge protocol and so on.
Further, we present simplification scheme for probabilistic and controlled teleportation of the unknown one-particle quantum state using the pure three-particle entangled state as the quantum chan- nel. Both special entangled state and non-maximum entangled state are used as quantum channels in the scheme. In addition, we also construct two efficient quantum logic networks for implementing the new scheme by means of the primitive operations.
Zero knowledge protocol is a basic method of cryptography. Its advantage is to keep others from pretending to be at the time of proving oneself, also to assure an useful information not to reveal. According to the basic thought of classical zero knowledge protoc- ol, we present a scheme for quantum zero knowledge protocol in group using a mode of quantum secure communication.
引文
[1]张永德,量子信息物理原理,北京:科学出版社, 2006.
[2]李承祖,黄明球,陈平形等,量子通信和量子计算,长沙:国防科技大学出版社,2000.
[3]喀兴林,高等量子力学 (第一版 ),北京:高等教育出版社,2001.
[4]王顺金,物理学前沿问题 (研究生系列教材 ),成都:四川大学出版社,2004.
[5]Wootters W. K., Zurek W. H., A single quantum cannot be cloned, Nature(London), 1982,299:802.
[6]戴葵,宋辉,刘芸等,量子信息技术引论,长沙:国防科技大学出版社,2001.
[7]Einstein A., Podolsky B., Rosen N., Can quantum mechanical description of physical reality be considered complete, Phys. Rev., 1935,47:777.
[8]张永德,吴盛俊,候广等,量子信息论——物理原理和某些进展,武汉:华中师范大学出版社,2001.
[9]Nielsen M. A., Chuang I. L., Quantum computation and quantum information, UK: Cambridge University Press, 2000.
[10]Deutsch D., Barenco A., Ekert A., Universality in quantum computation, Proc. R. Soc. Lond. A,1995,449:669.
[11]曾贵华,量子密码学(信息安全国家重点实验室信息安全丛书),北京:科学出版社,2006.
[12]Bennett C. H., Wiesner S. J., Communication via one- and two- particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett., 1992,69(20):2881.
[13]Mattle K., Weinfurter H., Kwiat P. G., et al., Dense coding in experimental quantum communication, Phys. Rev. Lett., 1996,76(25):4656.
[14]Bennett C. H., Brasard G., Crepeau C., et al., Teleporting an unknown quantum state via dual classical and Einstein-Podosky- Rosen channels, Phys. Rev. Lett., 1993,70(13):1895.
[15]Zukowski M., Zeilinger A., Horne A., et al., Event-ready- detectors Bell experiment via entanglement swapping, Phys. Rev. Lett., 1993,70(26):4287.
[16]Wiesner S., Conjugate coding, Sigact News, 1983,15(1):78.
[17]Bennett C. H., Brassard G., Quantum cryptography: public key distribution and coin tossing, Proc. IEEE Internat. Conf., 1984, 175.
[18]Bennett C. H., Quantum cryptography using any two nonorthogonal states, Phys. Rev. Lett., 1992,68(21):3121.
[19]Ekert A. K., Quantum cryptography based on Bell’s theorem, Phys. Rev. Lett., 1991,67(6):661.
[20]D’ Ariano G. M., Yuen H. P., Impossible of measuring the wave function of a single quantum system, Phys. Rev. Lett., 1996,76(16):2832.
[21]Hillery M., Bu z ek V., Berthiaume A., Quantum secret sharing, Phys. Rev. A, 1999,59(3):1829.
[22]Chen Y. A., Zhang A. N., Zhao Z., et al., Experimental quantum secret sharing and third-man quantum cryptography, ArXiv: quant-ph/0502131.
[23]Yan F. L., Gao T., Quantum secret sharing between multiparty and multiparty without entanglement, Phys. Rev. A, 2005,72(1):012304.
[24]Yan F. L., Gao T., Li Y. C., Quantum secret sharing between multiparty and multiparty with four states, ArXiv: quant-ph/0601191.
[25]Gao T., Yan F. L., Li Y. C., Quantum secret sharing between m-party and n-party with six states, ArXiv:quant-ph/0601111.
[26]Deng F. G., Zhou H. Y., Long G. L., Circular quantum secret sharing, ArXiv:quant-ph/0612018.
[27]Song J., Zhang S., Secure quantum secret sharing based on reusable GHZ states as secure carriers, Chin. Phys. Lett., 2006, 23(6):1383.
[28]Deng F. G., Li X. H., Chen P., et al., Fake-signal-and-cheating attack on quantum secret sharing, ArXiv:quant-ph/0604060.
[29]Tittel W., Zbinden H., Gisin N., Experimental demonstration of quantum secret sharing, Phys. Rev. A, 2001,63(4):042301.
[30]Beige A., Englert B.G., Kurtsiefer C., et al., Secure communication with a publicly known key, Acta Phys. Pol. A, 2002,101(6):357.
[31]Beige A., Englert B.G., Kurtsiefer C., et al., Secure communication with single-photon two-qubit states, J. Phys. A: Math. Gen., 2002,35(28):407.
[32]Bostr o m K., Secure direct communication using entanglement, AriXv:quant-ph/0203064.
[33]Bostr o m K., Felbinger T., Deterministic secure direct communication using entanglement, Phys. Rev. Lett., 2002, 89(18):187902.
[34]Deng F. G., Long G. L., Liu X. S., Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block, Phys. Rev. A, 2003,68(4):042317.
[35]Yang L., Quantum no-key protocol for direct and secure transmission of quantum and classical messages, ArXiv: quant-ph/0309200.
[36]Deng F. G., Long G. L., Secure direct communication protocol with a quantum one-time pad, Phys. Rev. A, 2004,69(5):052319.
[37]Cai Q. Y., Li B. W., Deterministic secure communication without using entanglement, Chin. Phys. Lett., 2004,21(4):601.
[38]Cai Q. Y., Deterministic secure direct communication using quantum non locality, ArXiv:quant-ph/0309108.
[39]Yan F. L., Zhang X. Q., Secure direct communication using Einstein-Podolsky-Rosen pairs and teleportation, ArXiv: quant-ph/0311132.
[40]Gao T., Yan F. L., Wang Z. X., Controlled quantum teleportation and secure direct communication, ArXiv: quant-ph/0403155.
[41]Gao T., Controlled and secure direct communication using GHZ state and teleportation, Z. Naturforsch. A, 2004,59(a):597.
[42]Gao T., Yan F. L. Wang Z. X., Quantum secure direct communication by Einstein-Podolsky-Rosen pairs and entanglement swapping, Nuovo Cimento B, 2004,119:313.
[43]Gao T., Yan F. L., Wang Z. X., Deterministic secure direct communication using GHZ states and swapping quantum entanglement, J. Phys. A, 2005,38:5761.
[44]Yan F. L., Gao T., A scheme for quantum communication using EPR pairs and local measurement, ArXiv: quant-ph/0501055.
[45]Deng F. G., Li X. H., Li C. Y., et al., Economical quantum secure direct communication network with single photons, ArXiv: quant-ph/0606008.
[46]Zeng G. H., Wang X. M., Quantum key distribution with authentication, ArXiv:quant-ph/9812022.
[47]Dusek M., Haderka O., Hendrych M., et al., Quantum identication system, Phys. Rev. A, 1999,60(1):149.
[48]Mlhara T., Quantum identification schemes with entanglements, Phys. Rev. A, 2002,65(5):1.
[49]Dam W. V., Comment on quantum identification schemes with entanglements, Phys. Rev. A., 2003,68(2):1.
[50]Zeng G. H., Guo G. C., Quantum authentication protocol, ArXiv:quant-ph/0001046.
[51]曾文杰,周南润,曾贵华,基于隐形传态的跨中心量子身份认证方案,光电子·激光,2005,16(1):94.
[52]温晓军,刘云,分布式量子通信网络中的身份认证方案,铁道学报,2005,27(6):58.
[53]杜建忠,朱甫臣,抵抗多次拦截攻击的量子密钥分发中的身份认证,北京邮电大学学报,2005,28(1):92.
[54]曾贵华,不依赖于第三方的动态量子身份认证方案,电子学报,2004,32(7):1148.
[55]Boumeester D., Pan J. W., Mattle K., et al., Experimental quantum teleportation, Nature (London), 1997,390(60):575.
[56]Yuan H. C., Qi K. G., Quantum logic networks for controlled teleportation of a single particle via W state, Chin. Phy., 2005,14(5):898.
[57]郑亦庄,戴玲玉,郭光灿,三粒子纠缠 W 态的隐形传态,物理学报,2003,52(11): 2678.
[58]Zhou J. D., Hou G., Wu S. J., et al., Controlled quantum teleportation, ArXiv:quant-ph/0006030.
[59]Xue Z. Y., Yi Y. M., Cao Z. L., Quantum teleportation of tripartite arbitrary via W State, Commun. Theor. Phys., 2005,44:1021.
[60]Yan F. L., Wang D., Probabilistic and controlled teleportation of unknown quantum states, Phys. Lett. A, 2003,316:297.
[61]王保如,闫凤利,三粒子任意自旋态的隐形传输,河北师范大学学报(自然科学版),2004,28(4):361.
[62]郑玉红,赵素倩,杜占乐等,多能级多粒子量子态的传输,河北师范大学学报(自然科学版),2003,26(2):141.
[63]Dai H. Y., Kuang L. M., Li C. Z., Probabilistic teleportation of an arbitrary three-level two-particle state and classical communication cost, Commun. Theor. Phys., 2005,44:40.
[64]Guo Z. Y., Fang J. X., Zhu S. Q., et al., Probabilistic teleportation of an arbitrary two-particle state and its quantum circuits, Commun. Theor. Phys., 2006,45(6):1013.
[65]Gao T., Quantum logic networks for probabilistic and controlled teleportation of unknown quantum states, Commun. Theor. Phys., 2004, 42(2):223.
[66]Gao T., Yan F. L., Wang Z. X., Quantum logic networks for probabilistic teleportation of many particle state of general form, Quantum Information and Computation, 2004,4(3):186.
[67]Gao T., Wang Z. X., Yan F. L., Quantum logic network for probabilistic teleportation of two-particle state in a general form, Chin. Phys. Lett., 2003,20(12):2094.
[68]查新未,三体纯态的纠缠度及其分类,西安交通大学学报 2006, 40(2):243.
[69]Goldwasser S., Micali S., Rackoff G., The knowledge complexity of interactive proofs-systems, Proc. 17th STOC, 1985:291.
[70]Long G. L., Liu X. S., Theoretically efficient high-capacity quantum-key-distribution scheme, Phys. Rev. A, 2002,65(3):032302.
[2]李承祖,黄明球,陈平形等,量子通信和量子计算,长沙:国防科技大学出版社,2000.
[3]喀兴林,高等量子力学 (第一版 ),北京:高等教育出版社,2001.
[4]王顺金,物理学前沿问题 (研究生系列教材 ),成都:四川大学出版社,2004.
[5]Wootters W. K., Zurek W. H., A single quantum cannot be cloned, Nature(London), 1982,299:802.
[6]戴葵,宋辉,刘芸等,量子信息技术引论,长沙:国防科技大学出版社,2001.
[7]Einstein A., Podolsky B., Rosen N., Can quantum mechanical description of physical reality be considered complete, Phys. Rev., 1935,47:777.
[8]张永德,吴盛俊,候广等,量子信息论——物理原理和某些进展,武汉:华中师范大学出版社,2001.
[9]Nielsen M. A., Chuang I. L., Quantum computation and quantum information, UK: Cambridge University Press, 2000.
[10]Deutsch D., Barenco A., Ekert A., Universality in quantum computation, Proc. R. Soc. Lond. A,1995,449:669.
[11]曾贵华,量子密码学(信息安全国家重点实验室信息安全丛书),北京:科学出版社,2006.
[12]Bennett C. H., Wiesner S. J., Communication via one- and two- particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett., 1992,69(20):2881.
[13]Mattle K., Weinfurter H., Kwiat P. G., et al., Dense coding in experimental quantum communication, Phys. Rev. Lett., 1996,76(25):4656.
[14]Bennett C. H., Brasard G., Crepeau C., et al., Teleporting an unknown quantum state via dual classical and Einstein-Podosky- Rosen channels, Phys. Rev. Lett., 1993,70(13):1895.
[15]Zukowski M., Zeilinger A., Horne A., et al., Event-ready- detectors Bell experiment via entanglement swapping, Phys. Rev. Lett., 1993,70(26):4287.
[16]Wiesner S., Conjugate coding, Sigact News, 1983,15(1):78.
[17]Bennett C. H., Brassard G., Quantum cryptography: public key distribution and coin tossing, Proc. IEEE Internat. Conf., 1984, 175.
[18]Bennett C. H., Quantum cryptography using any two nonorthogonal states, Phys. Rev. Lett., 1992,68(21):3121.
[19]Ekert A. K., Quantum cryptography based on Bell’s theorem, Phys. Rev. Lett., 1991,67(6):661.
[20]D’ Ariano G. M., Yuen H. P., Impossible of measuring the wave function of a single quantum system, Phys. Rev. Lett., 1996,76(16):2832.
[21]Hillery M., Bu z ek V., Berthiaume A., Quantum secret sharing, Phys. Rev. A, 1999,59(3):1829.
[22]Chen Y. A., Zhang A. N., Zhao Z., et al., Experimental quantum secret sharing and third-man quantum cryptography, ArXiv: quant-ph/0502131.
[23]Yan F. L., Gao T., Quantum secret sharing between multiparty and multiparty without entanglement, Phys. Rev. A, 2005,72(1):012304.
[24]Yan F. L., Gao T., Li Y. C., Quantum secret sharing between multiparty and multiparty with four states, ArXiv: quant-ph/0601191.
[25]Gao T., Yan F. L., Li Y. C., Quantum secret sharing between m-party and n-party with six states, ArXiv:quant-ph/0601111.
[26]Deng F. G., Zhou H. Y., Long G. L., Circular quantum secret sharing, ArXiv:quant-ph/0612018.
[27]Song J., Zhang S., Secure quantum secret sharing based on reusable GHZ states as secure carriers, Chin. Phys. Lett., 2006, 23(6):1383.
[28]Deng F. G., Li X. H., Chen P., et al., Fake-signal-and-cheating attack on quantum secret sharing, ArXiv:quant-ph/0604060.
[29]Tittel W., Zbinden H., Gisin N., Experimental demonstration of quantum secret sharing, Phys. Rev. A, 2001,63(4):042301.
[30]Beige A., Englert B.G., Kurtsiefer C., et al., Secure communication with a publicly known key, Acta Phys. Pol. A, 2002,101(6):357.
[31]Beige A., Englert B.G., Kurtsiefer C., et al., Secure communication with single-photon two-qubit states, J. Phys. A: Math. Gen., 2002,35(28):407.
[32]Bostr o m K., Secure direct communication using entanglement, AriXv:quant-ph/0203064.
[33]Bostr o m K., Felbinger T., Deterministic secure direct communication using entanglement, Phys. Rev. Lett., 2002, 89(18):187902.
[34]Deng F. G., Long G. L., Liu X. S., Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block, Phys. Rev. A, 2003,68(4):042317.
[35]Yang L., Quantum no-key protocol for direct and secure transmission of quantum and classical messages, ArXiv: quant-ph/0309200.
[36]Deng F. G., Long G. L., Secure direct communication protocol with a quantum one-time pad, Phys. Rev. A, 2004,69(5):052319.
[37]Cai Q. Y., Li B. W., Deterministic secure communication without using entanglement, Chin. Phys. Lett., 2004,21(4):601.
[38]Cai Q. Y., Deterministic secure direct communication using quantum non locality, ArXiv:quant-ph/0309108.
[39]Yan F. L., Zhang X. Q., Secure direct communication using Einstein-Podolsky-Rosen pairs and teleportation, ArXiv: quant-ph/0311132.
[40]Gao T., Yan F. L., Wang Z. X., Controlled quantum teleportation and secure direct communication, ArXiv: quant-ph/0403155.
[41]Gao T., Controlled and secure direct communication using GHZ state and teleportation, Z. Naturforsch. A, 2004,59(a):597.
[42]Gao T., Yan F. L. Wang Z. X., Quantum secure direct communication by Einstein-Podolsky-Rosen pairs and entanglement swapping, Nuovo Cimento B, 2004,119:313.
[43]Gao T., Yan F. L., Wang Z. X., Deterministic secure direct communication using GHZ states and swapping quantum entanglement, J. Phys. A, 2005,38:5761.
[44]Yan F. L., Gao T., A scheme for quantum communication using EPR pairs and local measurement, ArXiv: quant-ph/0501055.
[45]Deng F. G., Li X. H., Li C. Y., et al., Economical quantum secure direct communication network with single photons, ArXiv: quant-ph/0606008.
[46]Zeng G. H., Wang X. M., Quantum key distribution with authentication, ArXiv:quant-ph/9812022.
[47]Dusek M., Haderka O., Hendrych M., et al., Quantum identication system, Phys. Rev. A, 1999,60(1):149.
[48]Mlhara T., Quantum identification schemes with entanglements, Phys. Rev. A, 2002,65(5):1.
[49]Dam W. V., Comment on quantum identification schemes with entanglements, Phys. Rev. A., 2003,68(2):1.
[50]Zeng G. H., Guo G. C., Quantum authentication protocol, ArXiv:quant-ph/0001046.
[51]曾文杰,周南润,曾贵华,基于隐形传态的跨中心量子身份认证方案,光电子·激光,2005,16(1):94.
[52]温晓军,刘云,分布式量子通信网络中的身份认证方案,铁道学报,2005,27(6):58.
[53]杜建忠,朱甫臣,抵抗多次拦截攻击的量子密钥分发中的身份认证,北京邮电大学学报,2005,28(1):92.
[54]曾贵华,不依赖于第三方的动态量子身份认证方案,电子学报,2004,32(7):1148.
[55]Boumeester D., Pan J. W., Mattle K., et al., Experimental quantum teleportation, Nature (London), 1997,390(60):575.
[56]Yuan H. C., Qi K. G., Quantum logic networks for controlled teleportation of a single particle via W state, Chin. Phy., 2005,14(5):898.
[57]郑亦庄,戴玲玉,郭光灿,三粒子纠缠 W 态的隐形传态,物理学报,2003,52(11): 2678.
[58]Zhou J. D., Hou G., Wu S. J., et al., Controlled quantum teleportation, ArXiv:quant-ph/0006030.
[59]Xue Z. Y., Yi Y. M., Cao Z. L., Quantum teleportation of tripartite arbitrary via W State, Commun. Theor. Phys., 2005,44:1021.
[60]Yan F. L., Wang D., Probabilistic and controlled teleportation of unknown quantum states, Phys. Lett. A, 2003,316:297.
[61]王保如,闫凤利,三粒子任意自旋态的隐形传输,河北师范大学学报(自然科学版),2004,28(4):361.
[62]郑玉红,赵素倩,杜占乐等,多能级多粒子量子态的传输,河北师范大学学报(自然科学版),2003,26(2):141.
[63]Dai H. Y., Kuang L. M., Li C. Z., Probabilistic teleportation of an arbitrary three-level two-particle state and classical communication cost, Commun. Theor. Phys., 2005,44:40.
[64]Guo Z. Y., Fang J. X., Zhu S. Q., et al., Probabilistic teleportation of an arbitrary two-particle state and its quantum circuits, Commun. Theor. Phys., 2006,45(6):1013.
[65]Gao T., Quantum logic networks for probabilistic and controlled teleportation of unknown quantum states, Commun. Theor. Phys., 2004, 42(2):223.
[66]Gao T., Yan F. L., Wang Z. X., Quantum logic networks for probabilistic teleportation of many particle state of general form, Quantum Information and Computation, 2004,4(3):186.
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