Universal collective rotation channels and quantum error correction

Journal of Mathematical Physics

Volumn 46, Issue 2, 2005, Pages

  Junge, Marius ^a   Kim, Peter T ^b   Kribs, David W ^b,c,d  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b UNIVERSITY OF GUELPH   (Canada)

^c UNIVERSITY OF WATERLOO   (Canada)

^d PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17044394723     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1824213     Document Type: Article

References (37)

1. Arveson, W., An Invitation to C*-Algebras, Graduate Texts in Mathematics, No. 39 (Springer-Verlag, New York, 1976).
2. Bacon, D., Chuang, I. L., and Harrow, A. W., "Efficient quantum circuits for Schur and Clebsch-Gordon transforms," quant-ph/0407082.
3. Bartlett, S. D., Rudolph, T., and Spekkens, R. W., "Decoherence-full subsystems and the cryptographic power of a private shared reference frame," Phys. Rev. A 70, 032307 (2004).
4. Bartlett, S. D., Rudolph, T., and Spekkens, R. W., "Classical and quantum communication without a shared reference frame," Phys. Rev. Lett. 91, 027901 (2003).
5. Boileau, J.-C., Gottesman, D., Laflamme, R., Poulin, D., and Spekkens, R. W., "Robust polarization-based quantum key distribution over collective-noise channel," Phys. Rev. Lett. 92, 017901 (2004).
6. Busch, P. and Singh, J., "Luders theorem for unsharp quantum effects," Phys. Lett. A 249, 10-24 (1998).
7. Choi, M. D., "Completely positive linear maps on complex matrices," Linear Algebr. Appl. 10, 285-290. (1975).
8. Cohen-Tannoudji, C., Diu, B., and Laloe, F., Quantum Mechanics, Volume One and Two (Wiley, Toronto, 1977).
9. Davidson, K. R., C*-Algebras by Example, Fields Institute Monographs Vol. 6 (American Mathematical Society, Providence, 1996).
10. Duan, L.-M., and Guo, G.-C. "Preserving coherence in quantum computation by pairing quantum bits," Phys. Rev. Lett. 79, 1953-1956 (1997).
11. De Filippo, S., "Quantum computation using decoherence-free states of the physical operator algebra," Phys. Rev. A 62, 052307 (2000).
12. Fortunato, E. M., Viola, L., Pravia, M. A., Knill, E., Laflamme, R., Havel, T. F., and Cory, D. G., "Exploring noiseless subsystems via nuclear magnetic resonance," Phys. Rev. A 67, 062303 (2003).
13. Fulton, W., and Harris, J., Representation Theory, A First Course (Springer-Verlag, New York, 1991).
14. n, Lecture Notes in Mathematics 830 (Springer-Verlag, New York, 1980).
15. Holbrook, J. A., Kribs, D. W., Laflamme, R., and Poulin, D., "Noiseless subsystems for collective rotation channels in quantum information theory," Integral Equ. Oper. Theory (to be published).
16. Holbrook, J. A., Kribs, D. W., and Laflamme, R., "Noiseless subsystems and the structure of the commutant in quantum error correction, " Quantum Inf. Process. 2, 381-419 (2003).
17. James, G. and Kerber, A., "The representation theory of the symmetric group," Encyclopedia of Mathematics and its Applications (Addison-Wesley Publishing, Toronto, 1981).
18. Kempe, J., Bacon, D., Lidar, D. A., and Whaley, K. B., "Theory of decoherence-free fault-tolerant universal quantum computation," Phys. Rev. A 63, 042307 (2001).
19. Knill, E., Laflamme, R., Ashikhmin, A., Barnum, H., Viola, L., and Zurek, W. H., "Introduction to quantum error correction," Los Alamos Sci., November 27, 2002.
20. Knill, E., Laflamme, R., and Viola, L., "Theory of quantum error correction for general noise," Phys. Rev. Lett. 84, 2525-2528 (2000).
21. Kraus, K., States, Effects and Operations: Fundamental Notions of Quantum Theory, Lecture Notes in Physics, Vol. 190 (Springer-Verlag, Berlin, 1983).
22. Kraus, K., "General state changes in quantum theory," Ann. Phys. (N.Y.) 64, 311-335 (1971).
23. Kribs, D. W. "A quantum computing primer for operator theorists," Linear Algebr. Appl. (to be published).
24. n," Proc. Edinb. Math. Soc. 46, 421-433 (2003).
25. Laflamme, R. (private communication).
26. Lidar, D. A., Chuang, I. L., and Whaley, K. B., "Decoherence free subspaces for quantum computation," Phys. Rev. Lett. 81, 2594-2597 (1998).
27. Nielsen, M. A., and Chuang, I. L., Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
28. Paulsen, V., Completely Bounded Maps and Operator Algebras (Cambridge University Press, Cambridge, United Kingdom, 2002).
29. Preskill, J., "Reliable quantum computers," Proc. R. Soc. London, Ser. A 454, 385-410 (1998).
30. Stinespring, W. F., "Positive functions on C*-algebras," Proc. Am. Math. Soc. 6, 211-216 (1955).
31. Takesaki, M., Theory of Operator Algebras I (Springer-Verlag, New York, 1979).
32. Viola, L., Knill, E., and Laflamme, R., "Constructing qubits in physical systems," J. Phys. A 34, 7067-7079 (2001).
33. Viola, L., Fortunato, E. M., Pravia, M. A., Knill, E., Laflamme, R., and Cory, D. G., "Experimental realization of noiseless subsystems for quantum information processing," Science 293, 2059-2063 (2001).
34. Zanardi, P., and Lloyd, S., "Topological protection and quantum noiseless subsystems," Phys. Rev. Lett. 90, 067902 (2003).
35. Zanardi, P., "Stabilizing quantum information," Phys. Rev. A 63, 012301 (2001).
36. Zanardi, P., and Rasetti, M., "Noiseless quantum codes," Phys. Rev. Lett. 79, 3306-3309 (1997).
37. Zarikian, V., "Algorithms for operator algebra calculations," Linear Algebr. Appl. (to be published).