任意先验概率下的两态概率量子克隆

量子电子学报 ›› 2019, Vol. 36 ›› Issue (4): 471-475.

任意先验概率下的两态概率量子克隆

张世军1，张文海2*

1 巢湖学院电子工程学院安徽巢湖238000； 2 淮南师范学院电子工程学院安徽淮南232038

收稿日期:2018-11-28 修回日期:2019-01-16 出版日期:2019-07-28 发布日期:2019-07-11
作者简介:张世军（1980-），安徽庐江人，硕士，讲师，主要从事量子信息和量子光学方面的研究。E-mail：zhangshijun19802004@aliyun.com
基金资助:
Supported by Natural Science Foundation of Education Department of Anhui Province of China (安徽高等学校自然科学研究项目, KJ2016A672)

Probabilistic quantum cloning of two states with arbitrary a prior probabilities

ZHANG Shijun 1 ， ZHANG Wenhai 2

1 School of Electronic Engineering, Chaohu University, Chaohu 238000, China； 2 School of Electronic Engineering, Huainan Normal University, Huainan 232038, China

Received:2018-11-28 Revised:2019-01-16 Published:2019-07-28 Online:2019-07-11

摘要/Abstract

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。

关键词: 量子信息, 量子克隆, 概率量子克隆, 平均失败概率, 最优确定性量子态区分

Abstract: 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 probabilities is given. The result shows that the the probabilistic quantum cloning converges to the optimal unambiguous quantum state discrimination as the number of copies goes to infinity. The average failure probability is dependent on a prior probabilities, this make 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.

Key words: quantum information, quantum cloning, probabilistic quantum cloning, average failure probability, optimal unambiguous quantum state discrimination

张世军1，张文海2*. 任意先验概率下的两态概率量子克隆[J]. 量子电子学报, 2019, 36(4): 471-475.

ZHANG Shijun 1,ZHANG Wenhai 2. Probabilistic quantum cloning of two states with arbitrary a prior probabilities[J]. Chinese Journal of Quantum Electronics, 2019, 36(4): 471-475.

参考文献

[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: 145. [3] Bu?ek V, Hillery M. Quantum copying: Beyond the no-cloning theorem [J]. Physical Review A，1996, 54: 1844-1852. [4] Duan Luming, Guo Guangcan. Probabilistic cloning and identification of linearly independent quantum states [J]. Physical Review Letters, 1998, 80: 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 low-intensity magnetic field [J]. Chinese Journal of Quantum 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: 318. [9] Zhang Wenhai, Wu Tao, Ye Liu, et al. Optimal real state cloning in d dimensions [J]. Physical Review A, 2007, 75: 044303. [10] Zhang Wenhai, Yu Longbao, Cao Zhuoliang, et al. Optimal cloning of two known nonorthogonal quantum states [J]. Physical Review A, 2012, 86: 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: 062310. [12] Zhang Chuanwei, Li Chuanfeng, Wang Ziyang, et al. Probabilistic quantum cloning via Greenberger-Horne-Zeilinger states [J]. Physical Review A, 2000, 62: 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] Jiménez O, Roa L, Delgado A. Probabilistic cloning of equidistant states [J]. Physical Review A, 2010, 82: 022328. [15] Jiménez O, Bergou J, Delgado A. Probabilistic cloning of three symmetric states [J]. Physical Review A, 2010, 82: 062307. [16] Zhang Wen, Rui Pinshu, Zhang Ziyun, et al. Probabilistically cloning two single-photon states using weak cross-Kerr nonlinearities [J]. New Journal of Physics, 2014, 16: 083019. [17] Chen Hongwei, Lu Dawei, Chong Bo, et al. Experimental demonstration of probabilistic quantum cloning [J]. Physical Review Letters, 2011, 106: 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.