Quantum error-correcting subsystems are unitarily recoverable subsystems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 74, Issue 4, 2006, Pages

  Kribs, David W ^a,b   Spekkens, Robert W ^c  

^a UNIVERSITY OF GUELPH   (Canada)

^b UNIVERSITY OF WATERLOO   (Canada)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; CRYSTAL STRUCTURE; ERROR CORRECTION; ITERATIVE METHODS;

CORRECTABLE SUBSYSTEM; NOISE OPERATION; NOISELESS SUBSYSTEMS;

QUANTUM THEORY;

EID: 33750387016     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.74.042329     Document Type: Article

References (32)

1. L. Viola, E. Knill, and R. Laflamme, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/35/331 34, 7067 (2001).
2. E. Knill, e-print quant-ph/0603252.
3. D. Kribs, R. Laflamme, and D. Poulin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.180501, 94, 180501 (2005).
4. D. W. Kribs, R. Laflamme, D. Poulin, and M. Lesosky, Quantum Inf. Comput. QICUAW 1533-7146 6, 382 (2006).
5. P. W. Shor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.52.R2493 52, R2493 (1995).
6. A. M. Steane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77. 793 77, 793 (1996).
7. D. Gottesman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.1862 54, 1862 (1996).
8. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.3824 54, 3824 (1996).
9. E. Knill and R. Laflamme, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.55.900 55, 900 (1997).
10. G. M. Palma, K.-A. Suominen, and A. Ekert, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 452, 567 (1996).
11. L.-M. Duan and G.-C. Guo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.1953 79, 1953 (1997).
12. P. Zanardi and M. Rasetti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.3306 79, 3306 (1997).
13. D. A. Lidar, I. L. Chuang, and K. B. Whaley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.2594 81, 2594 (1998).
14. E. Knill, R. Laflamme, and L. Viola, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2525 84, 2525 (2000).
15. P. Zanardi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.012301 63, 012301 (2001).
16. J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.042307 63, 042307 (2001).
17. D. Bacon, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.012340 73, 012340 (2006).
18. D. Poulin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95. 230504 95, 230504 (2005).
19. A. Klappenecker and P. Kiran Sarvepalli, e-print quant-ph/0604161.
20. M. D. Choi and D. W. Kribs, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.039905 96, 050501 (2006).
21. M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
22. A. Nayak and P. Sen, Quantum Inf. Comput. QICUAW 1533-7146 (to be published).
23. M. A. Nielsen and D. Poulin, e-print quant-ph/0506069.
24. M. A. Nielsen, C. M. Caves, B. Schumacher, and H. Barnum, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 454, 277 (1997).
25. D. W. Kribs, Proc. Edinb. Math. Soc. PEMSA3 0013-0915 10.1017/S0013091501000980 46, 421 (2003).
26. J. A. Holbrook, D. W. Kribs, and R. Laflamme, Quantum Inf. Process. QIPUAT 1570-0755 10.1023/B:QINP.0000022737.53723.b4 2, 381 (2004).
27. M. D. Choi, D. W. Kribs, and K. Życzkowski, Rep. Math. Phys. RMHPBE 0034-4877 58, 77 (2006).
28. R. Blume-Kohout, Ph.D. thesis, Berkeley, 2005 (unpublished).
29. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities (Cambridge University Press, Cambridge, England, 1934).
30. R. Bhatia, Matrix Analysis (Springer, New York, 1997).
31. A. Uhlmann, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01609834 54, 21 (1977).
32. I. Bengtsson and K. Życzkowski, Geometry of Quantum States (Cambridge University Press, Cambridge, England, 2006).