Existence and construction of simultaneous cloning machines for mixed states
详细信息 查看全文
- 作者：ZhiHua Guo ; HuaiXin Cao ; ShiXian Qu
- 关键词：simultaneous cloning machine ; quantum channel ; mixed state ; 040302
- 刊名：SCIENCE CHINA Physics, Mechanics & Astronomy
- 出版年：2015
- 出版时间：April 2015
- 年：2015
- 卷：58
- 期：4
- 页码：1-5
- 全文大小：265 KB
- 参考文献：1. Wooters WK, Zurek WH. A single quantum cannot be cloned. Nature, 1982, 299: 802-03 CrossRef
2. Barnum H, Caves C M, Fuchs C A, et al. Noncommuting mixed states cannot be broadcast. Phys Rev Lett, 1996, 76: 2818-821 CrossRef
3. Bru? D. Optimal eavesdropping in quantum cryptography with six states. Phys Rev Lett, 1998, 81: 3018-021 CrossRef
4. Duan LM, Guo G C. Probabilistic cloning and identification of linearly independent quantum states. Phys Rev Lett, 1998, 80: 4999 CrossRef
5. Duan L M, Guo G C. A probabilistic cloning machine for replicating two non-orthogonal states. Phys Lett A, 1998, 243: 261-64 CrossRef
6. Piani M, Horodecki P, Horodecki R. No-local-broadcasting theorem for multipartite quantum correlations. Phys Rev Lett, 2008, 100: 090502 CrossRef
7. Luo S L, Li N. Relation between “no broadcasting-for noncommuting states and “no local broadcasting-for quantum correlations. Phys Rev A, 2009, 79: 054305 CrossRef
8. Zhang W H, Yu L B, Yang M, et al. Quantum cloning with multicopy in / d-dimensions. Sci China-Phys Mech Astron, 2011, 54: 2217-224 CrossRef
9. Fan H, Liu B Y, Shi K J. Quantum cloning of identical mixed qubits. Quantum Inf Comput, 2007, 7: 551-58
10. Fan H, Wang Y N, Jing L, et al. Quantum cloning machines and the applications. arXiv:1301.2956v3
11. Shen Y, Hao L, Long G L. Why can we copy classical information? Chin Phys Lett, 2011, 28: 010306 CrossRef
12. Liu Y. Deleting a marked state in quantum database in a duality computing mode. Chin Sci Bull, 2013, 58: 2927-931 CrossRef
13. Liu Y, Ouyang X P. A quantum algorithm that deletes marked states from an arbitrary database. Chin Sci Bull, 2013, 58: 2329-333 CrossRef
14. Long Y, Feng G R, Pearson J, et al. Experimental quantum deletion in an NMR quantum information processor. Sci China-Phys Mech Astron, 2014, 57: 1256-261 CrossRef
15. Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. London: Cambridge University Press, 2000
16. Long G L. The general quantum interference principle and the duality computer. Commun Theor Phys, 2006, 45: 825-43 CrossRef
17. Gudder S. Mathematical theory of duality quantum computers. Quantum Inf Proc, 2007, 6: 37-8 CrossRef
18. Zou X F, Qiu DW, Wu L H, et al. On mathematical theory of the duality computers. Quantum Inf Proc, 2009, 8: 37-0 CrossRef
19. Long G L. Mathematical theory of the duality computer in the density matrix formalism. Quantum Inf Proc, 2007, 6: 49-3 CrossRef
20. Wang W Y, Shang B, Wang C, et al. Prime factorization in the duality computer. Commun Theor Phys, 2007, 47: 471-72 CrossRef
21. Long G L. Duality quantum computing and duality quantum information processing. Int J Theor Phys, 2011, 50: 1305-318
文摘
It is a well-known fact that the no-cloning theorem forbids the creation of identical copies of an arbitrary unknown quantum state. In other words, there does not exist a quantum cloning machine that can clone all quantum states. However, it is possible to clone given quantum states under certain conditions, for instance, k distinct pure states |Ψ 1? |Ψ 2? - |Ψ k ?can be cloned simultaneously if and only if they are orthogonal. This paper discusses the existence and construction of simultaneous cloning machines for mixed states. It is proved that k distinct mixed states ρ 1, ρ 2, - ρ k of the n-dimensional quantum system ?sup class="a-plus-plus"> n can be cloned simultaneously, that is, there exists a quantum channel Φ on M n ⊿M n and a state Σ in M n , such that Φ(ρ i ⊿Σ) = ρ i ⊿ρ i for all i, if and only if ρ i ρ j = 0 (i ?j). Also, the constructing procedure of the desired simultaneous cloning machine is given.