连续变量量子克隆
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摘要
量子态不可克隆是量子力学的固有特性,它为量子克隆设置了一个不可逾越的界限;同时量子态不可精确复制也是量子密码术的重要前提,它确保了量子密码的安全性,使得窃听者不可能采取克隆技术来获得合法用户的信息。因而,量子不可克隆定理是量子信息科学的重要理论基础之一。近年来,人们对它作了进一步的研究,揭示出更丰富的物理内涵。之后,科学家们逐渐发现量子克隆不仅能够改善一些量子计算方案,而且对连续变量相干态的量子密钥分发是最优的窃听方案,连续变量量子克隆已成为量子信息网络中非常重要的内容之一。因此,对连续变量量子态的克隆的研究有着非常重要的意义。
本文的主要工作如下:
(1)连续变量纠缠态量子克隆的理论研究。在段路明等人提出的连续变量纠缠不可分判据以及Weedbrook等人提出的(Local e-cloner和Global e-cloner)两种纠缠态的克隆方案的基础上,用纠缠不可分判据对两种纠缠态的克隆方案克隆得到的纠缠态的纠缠特性进行了分析,从理论上分析了入射和出射分束器的反射率可变情况下的非对称Local e-cloner方案,证明了此克隆方案得到的两组纠缠态分别在分束器的反射率大于50%和小于50%时出现纠缠特性不对称的量子纠缠。
(2)连续变量相干态量子克隆的实验研究。首先在理论上,分析了利用非简并光学参量振荡器(NOPA)实现量子克隆以及利用分束器和平衡零拍探测系统实现量子克隆两种连续变量相干态的量子克隆方案。在此基础上,我们分析了利用纠缠态实现可控连续变量量子克隆的实验方案。接着,采用线性量子克隆方案对连续变量相干态的量子克隆进行了实验研究,并且成功实现了相干态的量子克隆;同时,也进行了利用EPR态填补真空通道的量子克隆实验研究。目前,我们已经完成了该实验装置的搭建,并且采用NOPA腔获得了-2.5dB的双模正交位相压缩光,完成了EPR态的制备工作。
The noncloning theorem is the intrinsic property of quantum mechanics, it has established an insurmountable boundary for quantum clones; simultaneously the quantum state which cannot duplicate precisely is also the important premise of quantum cryptography, it had guaranteed the quantum password's security which causes the eavesdropping attackers not to be impossible to adopt quantum clones to obtain the information of the validated user. So, the noncloning theorem is one of the most important theory of the quantum information field. In recent years, scientists have done the further research and promulgates the richer physical connotation. Afterward, it has been shown that quantum cloning might improve the performance of some quantum computational tasks,and it is believed to be the optimal eavesdropping attack for a certain class of quantum key distribution protocols employing coherent states. The continuous variable (CV) quantum cloning is also one of very important contents in the quantum information network. Governed by these motivations, it has the very vital significance to the CV quantum state's clone's research.
The main works of this dissertation are as follows:
(1) The theoretical research of the CV entanglement's quantum clone. First we introduced the CV entanglement inseparable criterion proposed by Duan Luming et al. and two kind of quantum entanglement cloning machine (Local e-cloner and Global e-cloner) proposed by Weedbrook et al. Then, we analyse the entanglement characteristic of two kind of clone machines' cloned entanglement with the entanglement inseparable criterion. Finally, we theoretically analyze the asymmetrical Local e-cloner when the reflection of the input and output beam splitters is R. It is proved that two cloned entangled states has the asymmetric entanglement characteristic using the entanglement inseparable criterion when the R is greater than 50% and less than 50% respectively.
(2) The experimental study of the CV coherent state's quantum clone. First,we theoretically analyze two kinds of CV coherent state's quantum cloning schemes, namely the quantum clone using the non-degeneration optics parameter oscillator (NOPA) and the quantum clone using the beam splitters and balanced homodyne detection. On the basis, we analyze the controlled CV quantum coherent state clone scheme with the EPR states. Then, we experimentally study the CV coherent state's quantum clone using the linear quantum cloning scheme and successfully realize the coherent state's quantum clone.At the same time, we continue the CV coherent state's quantum clone experiment which will be filled by the EPR entanglement in two vacuum passages.Now, we had completed the building of the clone scheme, prepared the EPR state and obtained the two-mode quadrature phase squeezed states of -4.5dB using the NOPA cavity.
本文的主要工作如下:
(1)连续变量纠缠态量子克隆的理论研究。在段路明等人提出的连续变量纠缠不可分判据以及Weedbrook等人提出的(Local e-cloner和Global e-cloner)两种纠缠态的克隆方案的基础上,用纠缠不可分判据对两种纠缠态的克隆方案克隆得到的纠缠态的纠缠特性进行了分析,从理论上分析了入射和出射分束器的反射率可变情况下的非对称Local e-cloner方案,证明了此克隆方案得到的两组纠缠态分别在分束器的反射率大于50%和小于50%时出现纠缠特性不对称的量子纠缠。
(2)连续变量相干态量子克隆的实验研究。首先在理论上,分析了利用非简并光学参量振荡器(NOPA)实现量子克隆以及利用分束器和平衡零拍探测系统实现量子克隆两种连续变量相干态的量子克隆方案。在此基础上,我们分析了利用纠缠态实现可控连续变量量子克隆的实验方案。接着,采用线性量子克隆方案对连续变量相干态的量子克隆进行了实验研究,并且成功实现了相干态的量子克隆;同时,也进行了利用EPR态填补真空通道的量子克隆实验研究。目前,我们已经完成了该实验装置的搭建,并且采用NOPA腔获得了-2.5dB的双模正交位相压缩光,完成了EPR态的制备工作。
The noncloning theorem is the intrinsic property of quantum mechanics, it has established an insurmountable boundary for quantum clones; simultaneously the quantum state which cannot duplicate precisely is also the important premise of quantum cryptography, it had guaranteed the quantum password's security which causes the eavesdropping attackers not to be impossible to adopt quantum clones to obtain the information of the validated user. So, the noncloning theorem is one of the most important theory of the quantum information field. In recent years, scientists have done the further research and promulgates the richer physical connotation. Afterward, it has been shown that quantum cloning might improve the performance of some quantum computational tasks,and it is believed to be the optimal eavesdropping attack for a certain class of quantum key distribution protocols employing coherent states. The continuous variable (CV) quantum cloning is also one of very important contents in the quantum information network. Governed by these motivations, it has the very vital significance to the CV quantum state's clone's research.
The main works of this dissertation are as follows:
(1) The theoretical research of the CV entanglement's quantum clone. First we introduced the CV entanglement inseparable criterion proposed by Duan Luming et al. and two kind of quantum entanglement cloning machine (Local e-cloner and Global e-cloner) proposed by Weedbrook et al. Then, we analyse the entanglement characteristic of two kind of clone machines' cloned entanglement with the entanglement inseparable criterion. Finally, we theoretically analyze the asymmetrical Local e-cloner when the reflection of the input and output beam splitters is R. It is proved that two cloned entangled states has the asymmetric entanglement characteristic using the entanglement inseparable criterion when the R is greater than 50% and less than 50% respectively.
(2) The experimental study of the CV coherent state's quantum clone. First,we theoretically analyze two kinds of CV coherent state's quantum cloning schemes, namely the quantum clone using the non-degeneration optics parameter oscillator (NOPA) and the quantum clone using the beam splitters and balanced homodyne detection. On the basis, we analyze the controlled CV quantum coherent state clone scheme with the EPR states. Then, we experimentally study the CV coherent state's quantum clone using the linear quantum cloning scheme and successfully realize the coherent state's quantum clone.At the same time, we continue the CV coherent state's quantum clone experiment which will be filled by the EPR entanglement in two vacuum passages.Now, we had completed the building of the clone scheme, prepared the EPR state and obtained the two-mode quadrature phase squeezed states of -4.5dB using the NOPA cavity.
引文
[1.1]曾谨言,《量子力学》卷Ⅱ,科学出版社,P35(2000)
[1.2]Einstein,B.Podolsky,and N.Rosen,Phys.Rev.47,777(1935)
[1.3]W.K.Wootters,W.H.Zurek,Nature,299(1982),802
[1.4]孙昌璞,“量子信息简介”,http://power.itp.ac.cn/suncp/quantum.htm
[1.5]李承祖等,《量子通讯与量子计算》,国防科技大学出版社,(2000)
[1.6]D.Juecks,Phys.Lett.A,92(1982),271
[1.7]H.P.Yuen,Phys.Lett.A,113(1986),405
[1.8]G.M.D'Ariano,H.P.Yuen,Phys.Rev.Lett,76(1996),2832
[1.9]H.Barnum,G.M.Caves,C.A.Fuchs,et.Al,Phys.Rev.Lett,76(1996),2818
[1.10]N.Gisin,B.Huttner,Phys.Lett.A,228(1997),13.
[1.11]M.A.Nielsen,L.L.Chuang,Phys.Rev.Lett,79(1997),321
[1.12]W.K.Wootters,W.H.Zurek,Nature,299(1982),802
[1.13]V.Scarani,S.Iblisdir,and N.Gisin,Rev.Mod.Phys.77,1225(2005)
[1.14]N.J.Cerfand S.Iblisdir,Phys.Rev.A 62,040301(R)(2000)
[1.15]M.Sabuncu,U.L.Andersen,and G.Leuchs,Phys.Rev.Lett.98,170503(2007)
[1.16]J.Fiurasek,Phys.Rev.Lett.86,4942(2001)
[1.17]U.L.Andersen,V.Josse,and G.Leuchs,Phys.Rev.Lett.94,240503(2005)
[1.18]J.Zhang,C.D.Xie,K.C.Peng,Phys.Rev.Lett.95,170501(2005)
[1.19]C.Weedbrook,N.B.Grosse,T.Symul,P.K.Lam,T.C.Ralp,Phys.Rev.A 77,052313(2008)
[1.20]孙跃,翟淑琴,张海龙,张俊香,郜江瑞,“连续变量量子纠缠态的非对称量子克隆”,量子光学学报,2009,15(2)
[2.1] E. F. Galvao and L. Hardy, Phys. Rev. A 62, 022301 (2000)
[2.2] F. Grosshans and N. Cerf, Phys. Rev. Lett 92, 047905 (2004)
[2.3] S. Braunstein et al., Phys. Rev. A 63, 052313 (2001)
[2.4] W. K. Wootters, W. H. Zurek, Nature, 299 (1982), 802
[2.5] V. Buzek and M. Hillery, Phys. Rev. A 54, 1844 (1996)
[2.6] V. Scarani, S. Iblisdir, and N. Gisin, Rev. Mod. Phys. 77, 1225 (2005)
[2.7] N. J. Cerf and S. Iblisdir, Phys. Rev. A 62, 040301 (R) (2000)
[2.8] M.Sabuncu, U. L. Andersen, and G. Leuchs, Phys. Rev. Lett. 98, 170503 (2007)
[2.9] J. Fiurasek , Phys.Rev.Lett. 86, 4942 (2001)
[2.10] S. L. Braunstein, N. J. Cerf et al., Phys. Rev. Lett. 86, 4938 (2001)
[2.11] U. L. Andersen, V. Josse, and G. Leuchs, Phys. Rev. Lett. 94, 240503 (2005)
[2.12] J. Zhang, C. D. Xie, K. C. Peng, Phys. Rev. Lett. 95, 170501 (2005)
[2.13] N. J. Cerf, A. Ipe, and X. Rottenberg, Phys. Rev. Lett. 85, 1754 (2000)
[2.14] G. M. D'Ariano, F. De Martini, and M. F. Sacchi, Phys. Rev. Lett. 86, 914 (2001)
[2.15] N. J. Cerf, S. Iblisdir, Phys. Rev. A 62, 040301 (R)
[2.16] E. Arthur and J. L. Kelly, Bell Syst. Tech. J. 44, 725 (1965)
[2.17] K. Hammerer et al., Phys. Rev. Lett. 94, 150503 (2005)
[2.18] P. K. Lam et al., Phys. Rev. Lett. 79, 1471 (1997)
[2.19] Jing Zhang, Kunchi Peng, Phys. Rev. A, 62, 064302 (2000)
[3.1]曾谨言,《量子力学》卷Ⅱ,科学出版社,P35(2000)
[3.2]V.Scarani,S.Iblisdir,and N.Gisin,Rev.Mod.Phys.77,1225(2005)
[3.3]N.J.Cerf and S.Iblisdir,Phys.Rev.A 62,040301(R)(2000)
[3.4]M.Sabuncu,U.L.Andersen,and G.Leuchs,Phys.Rev.Lett.98,170503(2007)
[3.5]J.Fiurasek,Phys.Rev.Lett.86,4942(2001)
[3.6]U.L.Andersen,V.Josse,and G.Leuchs,Phys.Rev.Lett.94,240503(2005)
[3.7]J.Zhang,C.D.Xie,K.C.Peng,Phys.Rev.Lett.95,170501(2005)
[3.8]C.Weedbrook,N.B.Grosse,T.Symul,P.K.Lam,T.C.Ralp,Phys.Rev.A 77,052313(2008)
[3.9]D.Walls and G.Milburn,Quantum Optics(Springer,Berlin,1994).
[3.10]L.M.Duan,G.Giedke,J.I.Cirac,and P.Zoller,Phys.Rev.Lett.84,2722(2000)
[4.1]K.Kato et al.,IEEE,J.Q.E.,Vol.QE-24,No.1,3(1988)
[4.2]A.Furusawa et al.,Science 282,706(1998)
[4.3]G.Leuch et al.,J.Mod.Opt.46,1927(1999)
[1.2]Einstein,B.Podolsky,and N.Rosen,Phys.Rev.47,777(1935)
[1.3]W.K.Wootters,W.H.Zurek,Nature,299(1982),802
[1.4]孙昌璞,“量子信息简介”,http://power.itp.ac.cn/suncp/quantum.htm
[1.5]李承祖等,《量子通讯与量子计算》,国防科技大学出版社,(2000)
[1.6]D.Juecks,Phys.Lett.A,92(1982),271
[1.7]H.P.Yuen,Phys.Lett.A,113(1986),405
[1.8]G.M.D'Ariano,H.P.Yuen,Phys.Rev.Lett,76(1996),2832
[1.9]H.Barnum,G.M.Caves,C.A.Fuchs,et.Al,Phys.Rev.Lett,76(1996),2818
[1.10]N.Gisin,B.Huttner,Phys.Lett.A,228(1997),13.
[1.11]M.A.Nielsen,L.L.Chuang,Phys.Rev.Lett,79(1997),321
[1.12]W.K.Wootters,W.H.Zurek,Nature,299(1982),802
[1.13]V.Scarani,S.Iblisdir,and N.Gisin,Rev.Mod.Phys.77,1225(2005)
[1.14]N.J.Cerfand S.Iblisdir,Phys.Rev.A 62,040301(R)(2000)
[1.15]M.Sabuncu,U.L.Andersen,and G.Leuchs,Phys.Rev.Lett.98,170503(2007)
[1.16]J.Fiurasek,Phys.Rev.Lett.86,4942(2001)
[1.17]U.L.Andersen,V.Josse,and G.Leuchs,Phys.Rev.Lett.94,240503(2005)
[1.18]J.Zhang,C.D.Xie,K.C.Peng,Phys.Rev.Lett.95,170501(2005)
[1.19]C.Weedbrook,N.B.Grosse,T.Symul,P.K.Lam,T.C.Ralp,Phys.Rev.A 77,052313(2008)
[1.20]孙跃,翟淑琴,张海龙,张俊香,郜江瑞,“连续变量量子纠缠态的非对称量子克隆”,量子光学学报,2009,15(2)
[2.1] E. F. Galvao and L. Hardy, Phys. Rev. A 62, 022301 (2000)
[2.2] F. Grosshans and N. Cerf, Phys. Rev. Lett 92, 047905 (2004)
[2.3] S. Braunstein et al., Phys. Rev. A 63, 052313 (2001)
[2.4] W. K. Wootters, W. H. Zurek, Nature, 299 (1982), 802
[2.5] V. Buzek and M. Hillery, Phys. Rev. A 54, 1844 (1996)
[2.6] V. Scarani, S. Iblisdir, and N. Gisin, Rev. Mod. Phys. 77, 1225 (2005)
[2.7] N. J. Cerf and S. Iblisdir, Phys. Rev. A 62, 040301 (R) (2000)
[2.8] M.Sabuncu, U. L. Andersen, and G. Leuchs, Phys. Rev. Lett. 98, 170503 (2007)
[2.9] J. Fiurasek , Phys.Rev.Lett. 86, 4942 (2001)
[2.10] S. L. Braunstein, N. J. Cerf et al., Phys. Rev. Lett. 86, 4938 (2001)
[2.11] U. L. Andersen, V. Josse, and G. Leuchs, Phys. Rev. Lett. 94, 240503 (2005)
[2.12] J. Zhang, C. D. Xie, K. C. Peng, Phys. Rev. Lett. 95, 170501 (2005)
[2.13] N. J. Cerf, A. Ipe, and X. Rottenberg, Phys. Rev. Lett. 85, 1754 (2000)
[2.14] G. M. D'Ariano, F. De Martini, and M. F. Sacchi, Phys. Rev. Lett. 86, 914 (2001)
[2.15] N. J. Cerf, S. Iblisdir, Phys. Rev. A 62, 040301 (R)
[2.16] E. Arthur and J. L. Kelly, Bell Syst. Tech. J. 44, 725 (1965)
[2.17] K. Hammerer et al., Phys. Rev. Lett. 94, 150503 (2005)
[2.18] P. K. Lam et al., Phys. Rev. Lett. 79, 1471 (1997)
[2.19] Jing Zhang, Kunchi Peng, Phys. Rev. A, 62, 064302 (2000)
[3.1]曾谨言,《量子力学》卷Ⅱ,科学出版社,P35(2000)
[3.2]V.Scarani,S.Iblisdir,and N.Gisin,Rev.Mod.Phys.77,1225(2005)
[3.3]N.J.Cerf and S.Iblisdir,Phys.Rev.A 62,040301(R)(2000)
[3.4]M.Sabuncu,U.L.Andersen,and G.Leuchs,Phys.Rev.Lett.98,170503(2007)
[3.5]J.Fiurasek,Phys.Rev.Lett.86,4942(2001)
[3.6]U.L.Andersen,V.Josse,and G.Leuchs,Phys.Rev.Lett.94,240503(2005)
[3.7]J.Zhang,C.D.Xie,K.C.Peng,Phys.Rev.Lett.95,170501(2005)
[3.8]C.Weedbrook,N.B.Grosse,T.Symul,P.K.Lam,T.C.Ralp,Phys.Rev.A 77,052313(2008)
[3.9]D.Walls and G.Milburn,Quantum Optics(Springer,Berlin,1994).
[3.10]L.M.Duan,G.Giedke,J.I.Cirac,and P.Zoller,Phys.Rev.Lett.84,2722(2000)
[4.1]K.Kato et al.,IEEE,J.Q.E.,Vol.QE-24,No.1,3(1988)
[4.2]A.Furusawa et al.,Science 282,706(1998)
[4.3]G.Leuch et al.,J.Mod.Opt.46,1927(1999)