Existence and construction of simultaneous cloning machines for mixed states

GUO ZhiHua 已出版文章查询
GUO ZhiHua
本平台内已出版文章查询
1 2 CAO HuaiXin 已出版文章查询
CAO HuaiXin
本平台内已出版文章查询
caohx@snnu.edu.cn
1 * QU ShiXian 已出版文章查询
QU ShiXian
本平台内已出版文章查询
3

+ 作者地址

1College of Mathematics and Information Science Shaanxi Normal University Xi'an 710062 China

2 College of Physics and Information Technology Shaanxi Normal University Xi'an 710062 China

3College of Physics and Information Technology Shaanxi Normal University Xi'an 710062 China


0
  • 摘要
  • 参考文献
  • 相关文章
  • 统计
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 |Ψ1>, |Ψ2>,..., |Ψk> 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 ρ1, ρ2,..., ρk of the n-dimensional quantum system Cn can be cloned simultaneously, that is, there exists a quantum channel Φ on MnMn and a state ∑ in Mn, such that Φ (ρi ⊗ ∑) = ρiρi for all i, if and only if ρiρj= 0 (i≠j). Also, the constructing procedure of the desired simultaneous cloning machine is given.

WootersWK, ZurekWH. A single quantum cannot be cloned. Nature,1982, 299: 802-803

Barnum H, Caves C M, Fuchs C A, et al. Noncommuting mixed states cannot be broadcast. Phys Rev Lett, 1996, 76: 2818-2821

Bruß D. Optimal eavesdropping in quantum cryptography with six states. Phys Rev Lett, 1998, 81: 3018-3021

Duan LM, Guo G C. Probabilistic cloning and identification of linearly independent quantum states. Phys Rev Lett, 1998, 80: 4999

Duan L M, Guo G C. A probabilistic cloning machine for replicating two non-orthogonal states. Phys Lett A, 1998, 243: 261-264

PianiM, Horodecki P, Horodecki R. No-local-broadcasting theorem for multipartite quantum correlations. Phys Rev Lett, 2008, 100: 090502

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

Zhang W H, Yu L B, Yang M, et al. Quantum cloning with multicopy in d-dimensions. Sci China-Phys Mech Astron, 2011, 54: 2217-2224

Fan H, Liu B Y, Shi K J. Quantum cloning of identical mixed qubits. Quantum Inf Comput, 2007, 7: 551-558

Fan H, Wang Y N, Jing L, et al. Quantum cloning machines and the applications. arXiv:1301.2956v3

Shen Y, Hao L, Long G L. Why can we copy classical information? Chin Phys Lett, 2011, 28: 010306

Liu Y. Deleting a marked state in quantum database in a duality computing mode. Chin Sci Bull, 2013, 58: 2927-2931

Liu Y, Ouyang X P. A quantum algorithm that deletes marked states from an arbitrary database. Chin Sci Bull, 2013, 58: 2329-2333

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: 1256-1261

Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. London: Cambridge University Press, 2000

Long G L. The general quantum interference principle and the duality computer. Commun Theor Phys, 2006, 45: 825-843

Gudder S. Mathematical theory of duality quantum computers. Quantum Inf Proc, 2007, 6: 37-48

Zou X F, Qiu DW,Wu L H, et al. On mathematical theory of the duality computers. Quantum Inf Proc, 2009, 8: 37-50

Long G L. Mathematical theory of the duality computer in the density matrix formalism. Quantum Inf Proc, 2007, 6: 49-53

Wang W Y, Shang B, Wang C, et al. Prime factorization in the duality computer. Commun Theor Phys, 2007, 47: 471-472

Long G L. Duality quantum computing and duality quantum information processing. Int J Theor Phys, 2011, 50: 1305-1318

Long G L, Liu Y,Wang C. Allowable generalized quantum gates. Commun Theor Phys, 2009, 51: 65-67

Du H K, Dou Y N. A spectral characterization for generalized quantum gates. J Math Phys, 2009, 50: 032101-032107

Wang Y Q, Du H K, Dou Y N. Note on generalized quantum gates and quantum operations. Int J Theor Phys, 2008, 47: 2268-2278

Cao H X, Li L, Chen Z L, et al. Restricted allowable generalized quantum gates. Chin Sci Bull, 2010, 55: 2122-2124

Zhang Y, Cao H X, Li L. Realization of allowable generalized quantum gates. Sci China-Phys Mech Astron, 2010, 53: 1878-1882

Cao H X, Chen Z L, Guo Z H, et al. Complex duality quantum computers acting on pure and mixed states. Sci China-Phys Mech Astron,2012, 55: 2452-2462

Cao H X, Long G L, Guo Z H, et al. Mathematical theory of generalized duality quantum computers acting on vector-states. Int J Theor Phys, 2013, 52: 1751-1767

Wu Z Q, Zhang S F, Zhu C X. Remarks on generalized quantum gates. Hacettepe J Math Stat, 2014, 43: 451-460

Choi M D. Completely positive linear maps on complex matrices. Linear Algebra Appl, 1975, 10: 285-290

Guo Z H, Cao H X. Existence and construction of a quantum channel with given inputs and outputs. Chin Sci Bull, 2012, 57: 4346-4350

Li C K, Poon Y T. Interpolation problem by completely positive maps. Linear Multlinear A, 2011, 59: 1159-1170


DOI: http://dx.doi.org/10.1007/s11433-014-5619-6

语种: 英文   

基金This work was supported by the National Natural Science Fo...

关键词simultaneous cloning machine quantum channel mixed state


期刊热词
  • + 更多
  • 字体大小