任意先验概率下的两态概率量子克隆
|
摘要
利用基本不等式,给出在任意先验概率下,两个量子态的概率m→n量子克隆的平均失败概率具体表达式。结果表明当拷贝的数目趋近无穷大时,概率量子克隆收敛为最优确定性量子态区分。平均失败概率依赖于先验概率,使得在一定的先验概率下总有一个量子态的拷贝不能获得。通过提高平均失败概率,在任意先验概率下总可以获得两个量子态的拷贝。
By exploring the basic inequality,the explicit expression of the average failure probability of the probabilistic m → n quantum cloning of two quantum states with arbitrary a prior probability is given.Results show that when the number of copies approaches infinity,the probabilistic quantum cloning converges to the optimal unambiguous quantum state discrimination.The average failure probability depends on a prior probability,which makes the copies of one of two states can not be always obtained for some a prior probability.By enhancing the average failure probability,the copies of two states can be always obtained for arbitrary a prior probability.
By exploring the basic inequality,the explicit expression of the average failure probability of the probabilistic m → n quantum cloning of two quantum states with arbitrary a prior probability is given.Results show that when the number of copies approaches infinity,the probabilistic quantum cloning converges to the optimal unambiguous quantum state discrimination.The average failure probability depends on a prior probability,which makes the copies of one of two states can not be always obtained for some a prior probability.By enhancing the average failure probability,the copies of two states can be always obtained for arbitrary a prior probability.
引文
[1]Wootters W K,Zurek W H.A single quantum cannot be cloned[J].Natural(London),1982,299:802-803.
[2]Gisin N,Ribordy G,Tittel W,et al. Quantum cryptography[J].Reviews of Modern Physics,2002,74(1):145-195.
[3]Buzek V,Hillery M.Quantum copying:Beyond the no-cloning theorem[J].Physical Review A,1996,54(3):1844-1852.
[4]Duan Luming,Guo Guangcan.Probabilistic cloning and identification of linearly independent quantum states[J].Physical Review Letters,1998,80(22):4999-5002.
[5]Zhao Jiaqiang,Cao Lianzhen,Yang Yang,et al. Nonlocality and robustness in two-photon entangled system[J].Chinese Journal of Quantum Electronics(量子电子学报),2018,35(4):451-454(in Chinese).
[6]Wang Qingliang,Ren Hengfeng.Research on quantum information transfer in spin chain with N=4 in lowintensity magnetic field[J].Chinese Journal of Q,uantum Electronics(量子电子学报)2018,35(4):439-443(in Chinese).
[7]Wu Tao,Fang Baolong,Ye Liu.Quantum cloning machines and their implementation in physical systems[J].Chinese Physics B,2013,22(11):110311.
[8]Zhang Wenhai,Ye Liu.Optimal asymmetric phase-covariant and real state cloning in d dimensions[J].New Journal of Physics,2007,9(9):318.
[9]Zhang Wenhai,Wu Tao,Ye Liu,et al. Optimal real state cloning in d dimensions[J].Physical Review A,2007,75(4):044303.
[10]Zhang Wenhai,Yu Longbao,Cao Zhuoliang,et al.Optimal cloning of two known nonorthogonal quantum states[J].Physical Review A,2012,86(2):022322.
[11]Zhang Chuanwei,Wang Ziyang,Li Chuanfeng,et al. Realizing probabilistic identification and cloning of quantum states via universal quantum logic gates[J].Physical Review A,2000,61(6):062310.
[12]Zhang Chuanwei,Li Chuanfeng,Wang Ziyang,et al. Probabilistic quantum cloning via Greenberger-HorneZeilinger states[J].Physical Review A,2000,62(4):042302.
[13]Zhang Wenhai,Dai Jielin,Cao Zhuoliang,et al. Probabilistic quantum cloning of real states[J].Optics Communications,2010,283(9):1956-1960.
[14]Jimenez O,Roa L,Delgado A.Probabilistic cloning of equidistant states[J].Physical Review A,2010,82(2):022328.
[15]Jim6nez O,Bergou J,Delgado A.Probabilistic cloning of three symmetric states[J].Physical Review A,2010,82(6):062307.
[16]Zhang Wen,Rui Pinshu,Zhang Ziyun,et al.Probabilistically cloning two single-photon states using weak crossKerr nonlinearities[J].New Journal of Physics,2014,16(8):083019.
[17]Chen Hongwei,Lu Dawei,Chong Bo,et al.Experimental demonstration of probabilistic quantum cloning[J].Physical Review Letters,2011,106(18):180404.
[18]Zhang Wenhai,Dai Jielin,Cao Zhuoliang,et al.Probabilistically perfect quantum cloning and unambiguous state discrimination[J].Optics Communications,2010,283(19):3818-3824.
[19]Zhang Wenhai,Yu Longbao,Cao Zhuoliang,et al. Maximum confidence measurements via probabilistic quantum cloning[J].Chinese Physics B,2013,22(3):030312.
[20]Barnett S M,Croke S.Quantum state discrimination[J].Advances in Optics and Photonics,2009,1(2):238-278.
[21]Sedlák M.Quantum theory of unambiguous measurements[J].Acta Physica Slovaca,2009,59(6):653-792.
[22]Bergou J A.Discrimination of quantum states[J].Journal of Modern Optics,2010,57(3):160-180.
[2]Gisin N,Ribordy G,Tittel W,et al. Quantum cryptography[J].Reviews of Modern Physics,2002,74(1):145-195.
[3]Buzek V,Hillery M.Quantum copying:Beyond the no-cloning theorem[J].Physical Review A,1996,54(3):1844-1852.
[4]Duan Luming,Guo Guangcan.Probabilistic cloning and identification of linearly independent quantum states[J].Physical Review Letters,1998,80(22):4999-5002.
[5]Zhao Jiaqiang,Cao Lianzhen,Yang Yang,et al. Nonlocality and robustness in two-photon entangled system[J].Chinese Journal of Quantum Electronics(量子电子学报),2018,35(4):451-454(in Chinese).
[6]Wang Qingliang,Ren Hengfeng.Research on quantum information transfer in spin chain with N=4 in lowintensity magnetic field[J].Chinese Journal of Q,uantum Electronics(量子电子学报)2018,35(4):439-443(in Chinese).
[7]Wu Tao,Fang Baolong,Ye Liu.Quantum cloning machines and their implementation in physical systems[J].Chinese Physics B,2013,22(11):110311.
[8]Zhang Wenhai,Ye Liu.Optimal asymmetric phase-covariant and real state cloning in d dimensions[J].New Journal of Physics,2007,9(9):318.
[9]Zhang Wenhai,Wu Tao,Ye Liu,et al. Optimal real state cloning in d dimensions[J].Physical Review A,2007,75(4):044303.
[10]Zhang Wenhai,Yu Longbao,Cao Zhuoliang,et al.Optimal cloning of two known nonorthogonal quantum states[J].Physical Review A,2012,86(2):022322.
[11]Zhang Chuanwei,Wang Ziyang,Li Chuanfeng,et al. Realizing probabilistic identification and cloning of quantum states via universal quantum logic gates[J].Physical Review A,2000,61(6):062310.
[12]Zhang Chuanwei,Li Chuanfeng,Wang Ziyang,et al. Probabilistic quantum cloning via Greenberger-HorneZeilinger states[J].Physical Review A,2000,62(4):042302.
[13]Zhang Wenhai,Dai Jielin,Cao Zhuoliang,et al. Probabilistic quantum cloning of real states[J].Optics Communications,2010,283(9):1956-1960.
[14]Jimenez O,Roa L,Delgado A.Probabilistic cloning of equidistant states[J].Physical Review A,2010,82(2):022328.
[15]Jim6nez O,Bergou J,Delgado A.Probabilistic cloning of three symmetric states[J].Physical Review A,2010,82(6):062307.
[16]Zhang Wen,Rui Pinshu,Zhang Ziyun,et al.Probabilistically cloning two single-photon states using weak crossKerr nonlinearities[J].New Journal of Physics,2014,16(8):083019.
[17]Chen Hongwei,Lu Dawei,Chong Bo,et al.Experimental demonstration of probabilistic quantum cloning[J].Physical Review Letters,2011,106(18):180404.
[18]Zhang Wenhai,Dai Jielin,Cao Zhuoliang,et al.Probabilistically perfect quantum cloning and unambiguous state discrimination[J].Optics Communications,2010,283(19):3818-3824.
[19]Zhang Wenhai,Yu Longbao,Cao Zhuoliang,et al. Maximum confidence measurements via probabilistic quantum cloning[J].Chinese Physics B,2013,22(3):030312.
[20]Barnett S M,Croke S.Quantum state discrimination[J].Advances in Optics and Photonics,2009,1(2):238-278.
[21]Sedlák M.Quantum theory of unambiguous measurements[J].Acta Physica Slovaca,2009,59(6):653-792.
[22]Bergou J A.Discrimination of quantum states[J].Journal of Modern Optics,2010,57(3):160-180.