Multiple-particle interference and quantum error correction

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 452, Issue 1954, 1996, Pages 2551-2577

  Steane, Andrew ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0007244732     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1996.0136     Document Type: Article

References (47)

1. Barenco, A. 1995 A universal two-bit gate for quantum computation. Proc. R. Soc. Lond. A 449, 679-683.
2. Bell, J. S. 1964 On the Einstein-Podolsky-Rosen paradox. Physics 1, 195-200. (
3. Reprinted in Bell, J. S. 1987 Speakable and unspeakable in quantum mechanics, pp. 14-21. Cambridge University Press.
4. ) Bennett, C. H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.. & Wootters, W. K. 1995 Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722-725.
5. Bernstein, E. & Vazirini, U. 1993 Quantum complexity theory. In Proc. 25th Annual ACM Symp. on the Theory of Computing, pp. 11-20. New York: Association for Computing Machinery.
6. Berthiaume A., Deutsch D. & Jozsa, R. 1994 The stabilisation of quantum computation. In Proc. Workshop on Physics and Computation, PhysComp 94, pp. 60-62. Los Alamitos: IEEE Computer Society Press.
7. Carmichael, H. J. 1991 An open systems approach to quantum optics. Lectures presented at l'Université Libre de Bruxelles, Bruxelles, Belgium, autumn 1991.
8. Cirac, J. I. & Zoller, P. 1995 Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091-4094.
9. Dalibard, J., Castin, Y. & Molmer, K. 1992 Wave-function approach to dissipative processes in quantum optics Phys. Rev. Lett. 68, 580-583.
10. Deutsch, D. 1985 Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400, 97-117.
11. Deutsch, D. & Jozsa, R. 1992 Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553-558.
12. Deutsch, D., Barenco, A. & Ekert, A. 1995 Universality in quantum computation. Proc. R. Soc. Lond. A 449, 669-677.
13. Deutsch, D., Ekert, A., Jozsa, R., Macchiavello, C., Popescu, S. & Sanpera, A. 1996 Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818-2821
14. DiVincenzo, D. P. 1995 Two-bit gates are universal for quantum computation. Phys. Rev. A 51, 1015-1022.
15. Dum, R., Zoller, P. & Ritsch, H. 1992 Phys. Rev. A 45, 4879.
16. Ekert, A. 1995 In Atomic Physics 14 (ed. D. J. Wineland, C. E. Wieman & S. J. Smith). New York: AIP Press.
17. Ekert, A. & Jozsa, R. 1996 Rev. Mod. Phys. 68, 733-753.
18. Feynman, R. P. 1982 Simulating physics with computers. Int. J. Theor. Phys. 21, 467-488.
19. Gilbert, E. N. 1952 A comparison of signalling alphabets. Bell Syst. Tech. J. 31, 504-522.
20. Gisin, N. 1984 Phys. Rev. Lett. 52, 1657;
21. Helvetica Phys. Acta 62, 363 (1989).
22. Greenberger, D. M., Hörne, M. A. & Zeilinger, A. 1989 Going beyond Bell's theorem. In Bell's theorem, quantum theory, and conceptions of the universe (ed. M. Kafatos), pp. 73-76. Dordrecht: Kluwer Academic Press.
23. Greenberger, D.M., Home, M. A., Shimony, A. & Zeilinger, A. 1990 Bell's theorem without inequalities. Am. J. Phys. 58, 1131-1143.
24. Hamming, R. W. 1950 Error detecting and error correcting codes. Bell Syst. Tech. J. 29, 147-160.
25. Hamming, R. W. 1986 Coding and information theory, 2nd edn. Englewood Cliffs: Prentice-Hall.
26. Hughes, R. J., Aide, D. M., Dyer, P., Luther, G. C., Morgan, G. L. & Schauer, M. 1995 Contemp. Phys. 36, 149-163.
27. Landauer, R. 1995 Phil. Trans. R. Soc. Lond. A 353, 367.
28. MacWilliams, F. J. & Sloane, N. J. A. 1977 The theory of error-correcting codes. Amsterdam: North Holland.
29. Palma, M. G., Suominen, K.-A. & Ekert, A. K. 1996 Proc. R. Soc. Lond. A 452, 567-584.
30. Mermin, N. D. 1990 Extreme quantum entanglement in a superposition of macroscopically distinct states. Phys. Rev. Lett. 65, 1838-1840.
31. M01mer, K., Castin Y. & Dalibard, J. 1993 Monte Carlo wave-function method in quantum optics. J. Opt. Soc. Am. B10, 524-538.
32. Pères, A. 1993 Quantum theory: concepts and methods. Dordrecht: Kluwer Academic Press.
33. Phoenix, S. J. D. & Townsend, P. D. 1995 Quantum cryptography: how to beat the code breakers using quantum mechanics. Contemp. Phys. 36, 165-195.
34. Schrödinger, E. 1935 Naturwiss. 23, 807.
35. (Translated in Quantum theory and measurement (ed. J. A. Wheeler & W. H. Zurek). Princeton University Press 1983.)
36. Schumacher, B. 1995 Quantum coding. Phys. Rev. A 51, 2738-2747.
37. Shimony, A. 1989 Conceptual foundations of quantum mechanics. In The new physics (ed. P. Davies) pp. 373-395. Cambridge University Press.
38. Shor, P. W. 1994 Algorithms for quantum computation: discrete logarithms and factoring. In Proc. 35th Annual Symp. on Foundations of Computer Science (ed. S. Goldwasser), pp. 124-134. Los Alamitos: IEEE Computer Society Press.
39. Shor, P. W. 1995 Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493-R2496.
40. Simon, D. 1994 On the power of quantum computation. In Proc. 35th Annual Symp. on Foundations of Computer Science (ed. S. Goldwasser), pp. 116-123. Los Alamitos: IEEE Computer Society Press.
41. Steane, A. M. 1996 Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793-797.
42. Turing, A. M. 1936 Proc. Land. Math. Soc. 243, 544.
43. Unruh, W. G. 1995 Maintaining coherence in quantum computers. Phys. Rev. A 51, 992-997.
44. Varshamov, R. R. 1957 Estimate of the number of signals in error correcting codes. Dokl. Akad. Nauk. SSSR 117, 739-741.
45. Zurek, W. H. 1981 Pointer basis of quantum apparatus: into what mixture does the wave packet collapse? Phys. Rev. D 24, 1516-1525.
46. Zurek, W. H. 1993 Preferred states, predictability, classicality and the environment-induced decoherence. Prog. Theor. Phys. 89, 281-312;
47. see also Zurek, W. H. 1991 Decoherence and the transition from quantum to classical, Physics Today 44 October, 36.