Quantum cloning in spin networks

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 70, Issue 6, 2004, Pages

  De Chiara, Gabriele ^a   Fazio, Rosario ^a   Macchiavello, Chiara ^b   Montangero, Simone ^a   Palma, G Massimo ^c  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b INFM   (Italy)

^c UNIVERSITY OF MILAN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CLONING; CRYPTOGRAPHY; DATA PROCESSING; HAMILTONIANS; LOGIC GATES; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; NETWORK PROTOCOLS; ROTATION; TOPOLOGY;

QUANTUM CLONING; QUANTUM GATES; QUANTUM NETWORKS; SPIN NETWORKS;

QUANTUM THEORY;

EID: 42749109082     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.70.062308     Document Type: Article

References (33)

1. M. Nielsen and I. Chuang, Quantum Computation and Quantum Communication (Cambridge University Press, Cambridge, England, 2000).
2. S. C. Benjamin and S. Bose, Phys. Rev. Lett. 90, 247901 (2003); M.-H. Yung, D. W. Leung, and S. Bose, Quantum Inf. Comput. 4, 174 (2004).
3. S. C. Benjamin and S. Bose, Phys. Rev. Lett. 90, 247901 (2003); M.-H. Yung, D. W. Leung, and S. Bose, Quantum Inf. Comput. 4, 174 (2004).
4. S. Bose, Phys. Rev. Lett. 91, 207901 (2003).
5. V. Subrahmanyam, Phys. Rev. A 69, 034304 (2004).
6. M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, Phys. Rev. Lett. 92, 187902 (2004).
7. F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. Lett. 92, 087201 (2004).
8. T. J. Osborne and N. Linden, Phys. Rev. A 69, 052315 (2004).
9. X. Wang, Phys. Rev. A 64, 012313 (2001); L. Amico, A. Osterloh, R Plastina, R. Fazio, and G. M. Palma, ibid. 69, 022304 (2004); S. Montangero, G. Benenti, and R. Fazio, Phys. Rev. Lett. 91, 187901 (2003).
10. X. Wang, Phys. Rev. A 64, 012313 (2001); L. Amico, A. Osterloh, R Plastina, R. Fazio, and G. M. Palma, ibid. 69, 022304 (2004); S. Montangero, G. Benenti, and R. Fazio, Phys. Rev. Lett. 91, 187901 (2003).
11. X. Wang, Phys. Rev. A 64, 012313 (2001); L. Amico, A. Osterloh, R Plastina, R. Fazio, and G. M. Palma, ibid. 69, 022304 (2004); S. Montangero, G. Benenti, and R. Fazio, Phys. Rev. Lett. 91, 187901 (2003).
12. W. K. Wootters and W. H. Zurek, Nature (London) 299, 802 (1982).
13. For a recent review on quantum cryptography, see N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74 145 (2002).
14. V. Bužek and M. Hillery, Phys. Rev. A 54, 1844 (1996).
15. D. Bruß, D. P. DiVincenzo, A. Ekert, C. A. Fuchs, C. Macchiavello, and J. A. Smolin, Phys. Rev. A 57, 2368 (1998).
16. N. Gisin and S. Massar, Phys. Rev. Lett. 79, 2153 (1997); D. Bruss, A. Ekert, and C. Macchiavello, ibid. 81, 2598 (1998); R. Werner, Phys. Rev. A 58, 1827 (1998).
17. N. Gisin and S. Massar, Phys. Rev. Lett. 79, 2153 (1997); D. Bruss, A. Ekert, and C. Macchiavello, ibid. 81, 2598 (1998); R. Werner, Phys. Rev. A 58, 1827 (1998).
18. N. Gisin and S. Massar, Phys. Rev. Lett. 79, 2153 (1997); D. Bruss, A. Ekert, and C. Macchiavello, ibid. 81, 2598 (1998); R. Werner, Phys. Rev. A 58, 1827 (1998).
19. D. Bruß, M. Cinchetti, G. M. D'Ariano, and C. Macchiavello, Phys. Rev. A 62, 012302 (2000).
20. H. K. Cummins, C. Jones, A. Furze, N. F. Soffe, M. Mosca, J. M. Peach, and J. A. Jones, Phys. Rev. Lett. 88, 187901 (2002).
21. A. Lama-Linares, C. Simon, J.-C. Howell, and D. Bouwmeester, Science 296, 712 (2002).
22. D. Pelliccia, V. Schettini, F. Sciarrino, C. Sias, and F. De Martini, Phys. Rev. A 68, 042306 (2003); F. De Martini, D. Pelliccia, and F. Sciarrino, Phys. Rev. Lett. 92, 067901 (2004).
23. D. Pelliccia, V. Schettini, F. Sciarrino, C. Sias, and F. De Martini, Phys. Rev. A 68, 042306 (2003); F. De Martini, D. Pelliccia, and F. Sciarrino, Phys. Rev. Lett. 92, 067901 (2004).
24. J. Du, T. Durt, P. Zou, L. C. Kwek, C. H. Lai, C. H. Oh, and A. Ekert, e-print quant-ph/0311010.
25. C.-S. Niu and R. B. Griffiths, Phys. Rev. A 60, 2764 (1999).
26. The model is invariant under rotations around the z axis so it is a natural candidate for a PCC. We also analyzed the case in which the XY symmetry is broken, the results for the fidelity were always much worse than for XY or Heisenberg models.
27. To find the evolution for the initial state, Eq. (2), we need to express it in the eigenstate basis. After some simple algebra one finds that |00...0〉=|(M+1)/2, (M+1)/2〉 and |10...0〉 = 1/√1+M|(M+1)/2, (M-1)/2〉-√M/√1+M|(M-1)/2, (M-1)/2〉.
28. -〉].
29. J. Fiurášek, Phys. Rev. A 67, 052314 (2003).
30. G. M. D'Ariano and C. Macchiavello, Phys. Rev. A 67, 042306 (2003).
31. V. Bužek, S. L. Braunstein, M. Hillery, and D. Bruß, Phys. Rev. A 56, 3446 (1997).
32. We refer to N. Schuch and J. Siewert, Phys. Rev. A 67, 032301 (2003) for the implementations of these circuits with time dependent XY model.
33. Yu. Makhlin, G. Schön and A. Shnirman, Rev. Mod. Phys. 73, 357 (2001).