Good quantum error-correcting codes exist

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 54, Issue 2, 1996, Pages 1098-1105

  Calderbank, A R ^a   Shor, Peter W ^a  

^a AT AND T LABS RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001398327     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.54.1098     Document Type: Article

References (17)

1. D. Deutsch, Proc. R. Soc. London Ser. A 400, 96 (1985); D. Simon, in Proceedings of the Thirty-Fifth Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society, Los Alamitos, CA, 1994) p. 116; P. W. Shor, ibid., p. 124; A. Ekert and R. Jozsa, Rev. Mod. Phys. (to be published).
2. S. Lloyd, Science 261, 1569 (1993); D. P. DiVincenzo, Phys. Rev. A 51, 1015 (1995); A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, Phys. Rev. Lett. 74, 4083 (1995); T. Sleator and H. Weinfurter, ibid. 74, 4087 (1995); I. L. Chuang and Y. Yamamoto, Phys. Rev. A 52, 3489 (1995).
3. J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74,, 4091 (1995).
4. W. G. Unruh, Phys. Rev. A 51,, 992 (1995).
5. G. M. Palma, K.-A. Suominen and A. K. Ekert, Proc. R. Soc. London A 452, 567 (1996).
6. R. Landauer, Philos. Trans. R. Soc. London, Ser. A 353, 367 (1995); R. Landauer, in Proceedings of the Drexel-4 Symposium on Quantum Nonintegrability — Quantum Classical Correspondence, edited by D. H. Feng and B.-L. Hu, (International Press, in press).
7. I. L. Chuang, R. Laflamme, P. W. Shor, and W. H. Zurek, Science 270,, 1635 (1995).
8. C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 75,, 4714 (1995).
9. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes (North-Holland, Amsterdam, 1977).
10. R. L. Dobrushin and S. I. Ortyukov, Probl. Peredachi Inf. 13, (1), 82 (1977) [Probl. Inf. Transm. (USSR) 13, 59 (1977)]; Probl. Peredachi Inf. 13 (3), 56 (1977) [Probl. Inf. Transm. (USSR) 13, 203 (1977)]; N. Pippenger, J. Assoc. Comput. Mach. 36, 531 (1989); N. Pippenger, G. D. Stamoulis, and J. N. Tsitsiklis, IEEE Trans. Inf. Theory 37, 639 (1991), U. Feige, P. Raghavan, D. Peleg, and E. Upfal, SIAM J. Comput. 23,1001 (1994).
11. W. K. Wooters and W. H. Zurek, Nature 299,, 802 (1982); D. Dieks, Phys. Lett. A 92,271 (1982).
12. P. W. Shor, Phys. Rev. A 52,, 2493 (1995).
13. L. B. Levitin, in Proceedings of the Fourth All-Union Conference on Information Theory, Tashkent (1969), p. 111, in Russian; A. S. Kholevo, Probl. Peredachi Inf. 9 (3), 3 (1973) [Probl. Inf. Transm. (USSR) 9, 177 (1973)].
14. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wooters, Phys. Rev. Lett. 76,, 722 (1996).
15. A. M. Steane, Proc. R. Soc. London Ser. A (to be published).
16. F. J. MacWilliams, N. J. A. Sloane, and J. G. Thompson, Discrete Math. 3,, 153 (1972).
17. B. Schumacher, Phys. Rev. A 51,, 2738 (1995); R. Jozsa and B. Schumacher, J. Mod. Opt. 41,2343 (1994).