Economical quantum cloning in any dimension

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 72, Issue 5, 2005, Pages

  Durt, Thomas ^a   Fiurášek, Jaromír ^b,c   Cerf, Nicolas J ^b  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^c PALACKÝ UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

CLONING MACHINES; D-DIMENSIONAL QUANTUM SYSTEM; QUBITS;

COMPUTATIONAL METHODS; FOURIER TRANSFORMS; INDUSTRIAL ECONOMICS; MACHINE COMPONENTS;

QUANTUM THEORY;

EID: 28844457004     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.72.052322     Document Type: Article

References (40)

1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.145 74, 145 (2002).
2. H.-K. Cummins, C. Jones, A. Furze, N-F Soffe, M. Mosca, J. M. Peach, and J-A Jones, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.187901 88, 187901 (2002).
3. N. Gisin, I. Marcikic, H. de Riedmatten, W. Tittel, and H. Zbinden, Nature (London) NATUAS 0028-0836 10.1038/nature01376 421, 509 (2003).
4. S. Gulde, M. Riebe, G. P-T Lancaster, C. Becher, J. Eschner, H. Häffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, Nature (London) NATUAS 0028-0836 10.1038/nature01336 421, 48 (2003).
5. J. Jones, Nature (London) NATUAS 0028-0836 10.1038/421029a 421, 29 (2003).
6. F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature (London) NATUAS 0028-0836 10.1038/nature01289 421, 238 (2003).
7. C. H. Bennett, and G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York, 1984), p. 175.
8. W. K. Wootters and W. H. Zurek, Nature (London) NATUAS 0028-0836 10.1038/299802a0 299, 802 (1982).
9. D. Dieks, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(82)90084-6 92, 271 (1982).
10. V. Buek and M. Hillery, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.1844 54, 1844 (1996).
11. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.127902 88, 127902 (2002);
12. M. Bourennane, A. Karlsson, G. BjÃrk, N. Gisin, and N. J. Cerf, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/47/307 35, 10065 (2002).
13. D. Bruss, M. Cinchetti, G. M. Dâariano, and C. Macchiavello, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.012302 62, 012302 (2000).
14. N. J. Cerf, T. Durt, and N. Gisin, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500340110109043 49, 1355 (2002).
15. H. Fan, K. Matsumoto, X.-B. Wang, and M. Wadati, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.012304 65, 012304 (2002).
16. H. Fan, H. Imai, K. Matsumoto, and X. B. Wang, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.022317 67, 022317 (2003).
17. A. T. Rezakhani, S. Siadatnejad, and A. H. Ghaderi, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2004.12.015 336, 278 (2005).
18. L.-P. Lamoureux and N. J. Cerf, Quantum Inf. Comput. QICUAW 1533-7146 5, 32 (2005).
19. C. A. Fuchs, N. Gisin, R. B. Griffiths, C.-S. Niu, and A. Peres, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.56.1163 56, 1163 (1997).
20. R. B. Griffiths and C.-S. Niu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.56.1173 56, 1173 (1997).
21. T. Durt, N. J. Cerf, N. Gisin, M. Zukowski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.012311 67, 012311 (2003).
22. T. Durt, D. Kaszlikowski, J-L Chen, and L-C Kwek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.032313 69, 032313 (2004).
23. A. K. Ekert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.661 67, 661 (1991).
24. J. Du, T. Durt, P. Zou, L. C. Kwek, C. H. Lai, C. H. Oh, and A. Ekert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.040505 94, 040505 (2005).
25. C-S. Niu and R. B. Griffiths, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.2764 60, 2764 (1999).
26. T. Durt and J. Du, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69. 062316 69, 062316 (2004).
27. F. Buscemi, G. M. DâAriano, and C. Macchiavello, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.042327 71, 042327 (2005).
28. A. Jamiolkowski, Rep. Math. Phys. RMHPBE 0034-4877 10.1016/0034-4877(72) 90011-0 3, 275 (1972).
29. M.-D. Choi, Linear Algebr. Appl. LAAPAW 0024-3795 10.1016/0024-3795(75) 90075-0 10, 285 (1975).
30. J. FiurÃÅek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.062310 64, 062310 (2001).
31. J. FiurÃÅek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.052314 67, 052314 (2003).
32. V. Buek and M. Hillery, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.5003 81, 5003 (1998).
33. R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.1827 58, 1827 (1998).
34. N. J. Cerf, Acta Phys. Slov. APSVCO 0323-0465 48, 115 (1998);
35. N. J. Cerf, J. Mod. Opt. JMOPEW 0950-0340 10.1080/095003400148141 47, 187 (2000).
36. N. J. Cerf, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.4497 84, 4497 (2000).
37. The deep reason for the appearance of Bell states in the formalism of cloning machines is the invariance with respect to the discrete Weyl-Heisenberg group (see G. Chiribella, G. M. DâAriano, P. Perinotti, and N. J. Cerf, quant-ph/0507130). In a paper in preparation, the role of a cyclic subgroup of this group will be analyzed in details. It will be shown that some restrictive assumptions must be made about the optimality of the cloner (see also Ref.).
38. S. Bandyopadhyay, P. O. Boykin, V. Roychowdhury, and F. Vatan, Algorithmica ALGOEJ 0178-4617 10.1007/s00453-002-0980-7 34, 512 (2002).
39. V. Buek, S. L. Braunstein, M. Hillery, and D. Bruss, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.56.3446 56, 3446 (1997).
40. G. M. DâAriano and C. Macchiavello, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.042306 67, 042306 (2003).