Equivalence classes of non-local unitary operations

Quantum Information and Computation

Volumn 2, Issue 3, 2002, Pages 240-254

  Dur W ^a   Cirac, J I ^b  

^a UNIVERSITY OF MUNICH   (Germany)

^b MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; INFORMATION SYSTEMS;

ARBITRARY OPERATORS; CLASSICAL COMMUNICATION; EQUIVALENCE RELATIONS; INTERCONVERSIONS; MULTIQUBIT SYSTEM; NON-ZERO PROBABILITY; PROBABILISTIC SIMULATION; UNITARY OPERATION;

EQUIVALENCE CLASSES;

EID: 0042222089     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (45)

1. D. Gottesman, quant-ph/9807006.
2. A. Chefles, C. R. Gilson and S. M. Barnett, quant-ph/0003062 and quant-ph/0006106.
3. J. Eisert, K. Jacobs, P. Papadopoulos and M. B. Plenio, Phys. Rev. A 62 052317 (2000).
4. D. Collins, N. Linden and S. Popescu, quant-ph/0005102
5. J. I. Cirac, W. Dür, B. Kraus and M. Lewenstein, Phys. Rev. Lett. 86, 544 (2001)
6. P. Zanardi, C. Zalka and L. Faoro, Phys. Rev. A 62, 30301R (2000)
7. W. Dür, G. Vidal, J. I. Cirac, N. Linden and S. Popescu, Phys. Rev. Lett. 87, 137901 (2001)
8. B. Kraus and J. I. Cirac, quant-ph 0011050
9. J. L. Dodd, M. A. Nielsen, M. J. Bremner, and R. T. Thew, quant-ph/0106064; M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, and C. M. Dawson quant-ph/0109064
10. J. L. Dodd, M. A. Nielsen, M. J. Bremner, and R. T. Thew, quant-ph/0106064; M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, and C. M. Dawson quant-ph/0109064
11. P. Wocjan, D. Janzing, Th. Beth, quant-ph/0106077; P. Wocjan, M. Roetteler, D. Janzing, Th. Beth, quant-ph/0109063; P. Wocjan, M. Roetteler, D. Janzing, Th. Beth, quant-ph/0109088.
12. P. Wocjan, D. Janzing, Th. Beth, quant-ph/0106077; P. Wocjan, M. Roetteler, D. Janzing, Th. Beth, quant-ph/0109063; P. Wocjan, M. Roetteler, D. Janzing, Th. Beth, quant-ph/0109088.
13. P. Wocjan, D. Janzing, Th. Beth, quant-ph/0106077; P. Wocjan, M. Roetteler, D. Janzing, Th. Beth, quant-ph/0109063; P. Wocjan, M. Roetteler, D. Janzing, Th. Beth, quant-ph/0109088.
14. C. H. Bennett, J. I. Cirac, M. S. Leifer, D. W. Leung, N. Linden, S. Popescu, and G. Vidal, quant-ph/0107035
15. D. W. Leung, quant-ph/0107041
16. G. Vidal and J. I. Cirac, quant-ph/0108076
17. G. Vidal and J. I. Cirac, quant-ph/0108076, quant-ph/0108077
18. W. Dür and J. I. Cirac, Phys. Rev. A 64, 012317 (2001).
19. C. H. Bennett, S. Popescu, D. Rohrlich, J.A. Smolin and A.V. Thapliyal, quant-ph/9908073;
20. W. Dür, G. Vidal and J. I. Cirac, Phys. Rev. A 62, 062314 (2000)
21. C. H. Bennett, H. J. Bernstein, S. Popescu and B. Schumacher, Phys. Rev. A 53, 2046(1996)
22. Einstein, Podolsky & Rosen, Phys. Rev. 47, 777-780 (1935); D. Bohm, Quantum Theorie, Prentice-Hall, Englewood Cliffs, New Jersey (1951).
23. Einstein, Podolsky & Rosen, Phys. Rev. 47, 777-780 (1935); D. Bohm, Quantum Theorie, Prentice-Hall, Englewood Cliffs, New Jersey (1951).
24. W. Dür, G. Vidal and J. I. Cirac, quant-ph/0112124
25. H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998); W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, Phys. Rev. A 59, 169-181 (1999).
26. H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998); W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, Phys. Rev. A 59, 169-181 (1999).
27. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin and W. K. Wootters, Phys. Rev. Lett. 76, 722 (1996); C. H. Bennett, D. P. DiVincenzo, J. A. Smolin and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).
28. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin and W. K. Wootters, Phys. Rev. Lett. 76, 722 (1996); C. H. Bennett, D. P. DiVincenzo, J. A. Smolin and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).
29. B
30. Throughout this paper, we will use gates and unitary operations synonymously.
31. G. Vidal, Journ. of Mod. Opt. 47, 355 (2000);
32. N. Linden and S. Popescu, Fortsch.Phys. 46, 567 (1998);
33. A. Sudbery, quant-ph/0001116;
34. H. A. Carteret and A. Sudbery, quant-ph/0001091;
35. J. Kempe, Phys. Rev. A60 910-916 (1999);
36. A. Acín, A. Andrianov, L. Costa, E. Jané, J. I. Latorre and R. Tarrach, Phys. Rev. Lett. 85, 1560 (2000); A. Ací, A. Andrianov, E. Jané, and R. Tarrach, J. Phys. A: Math. Gen. 34, 6725 (2001).
37. A. Acín, A. Andrianov, L. Costa, E. Jané, J. I. Latorre and R. Tarrach, Phys. Rev. Lett. 85, 1560 (2000); A. Ací, A. Andrianov, E. Jané, and R. Tarrach, J. Phys. A: Math. Gen. 34, 6725 (2001).
38. F. Verstraete, J. Dehaene, B. De Moor, H. Verschelde, quant-ph/0109033
39. N. Khaneja, R. Brockett and S. J. Glaser, Phys. Rev. A 63, 032308 (2001)
40. The uniqueness of this decomposition can easily derived using the results of Ref. [8].
41. G. Vidal, private communication
42. F. Verstraete, private communication.
43. F. Verstraete, J. Dehaene and B. De Moor, quant-ph/0105090.
44. A. Acin, E. Jane, and G. Vidal, Phys. Rev. A 64, 050302(R) (2001).
45. A. Acin, Phys. Rev. Lett 87, 177901 (2001).