Choice of measurement sets in qubit tomography

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 78, Issue 5, 2008, Pages

  De Burgh, Mark D ^a   Langford, Nathan K ^a   Doherty, Andrew C ^a   Gilchrist, Alexei ^b  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b MACQUARIE UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

DIAGNOSTIC RADIOGRAPHY; MAXIMUM LIKELIHOOD ESTIMATION; MEDICAL IMAGING; TOMOGRAPHY;

ASYMPTOTIC BOUNDS; FIXED SETS; MAXIMUM LIKELIHOOD TOMOGRAPHIES; MEASUREMENT SETS; OVER COMPLETE; PLATONIC SOLIDS; PROJECTIVE MEASUREMENTS; QUANTUM STATE TOMOGRAPHIES; QUBIT STATES; QUBIT TOMOGRAPHIES; TOMOGRAPHIC RECONSTRUCTIONS;

MEASUREMENTS;

EID: 57149092312     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.78.052122     Document Type: Article

References (51)

1. K. Vogel and H. Risken, Phys. Rev. A 40, 2847 (1989). 10.1103/PhysRevA.40.2847
2. U. Leonhardt, Phys. Rev. Lett. 74, 4101 (1995). 10.1103/PhysRevLett.74. 4101
3. A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, Phys. Rev. Lett. 83, 3103 (1999). 10.1103/PhysRevLett.83.3103
4. N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O'Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, Phys. Rev. Lett. 93, 053601 (2004). 10.1103/PhysRevLett.93.053601
5. H. Häeffner, W. Häensel, C. F. Roos, J. Benhelm, D. C. al kar, M. Chwalla, T. Köerber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, Nature 438, 643 (2005). 10.1038/nature04279
6. R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, Nature 443, 838 (2006). 10.1038/nature05146
7. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).
8. S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995). 10.1103/PhysRevLett.74.1259
9. R. Derka, V. Buzek, and A. K. Ekert, Phys. Rev. Lett. 80, 1571 (1998). 10.1103/PhysRevLett.80.1571
10. G. Vidal, J. I. Latorre, P. Pascual, and R. Tarrach, Phys. Rev. A 60, 126 (1999). 10.1103/PhysRevA.60.126
11. J. I. Latorre, P. Pascual, and R. Tarrach, Phys. Rev. Lett. 81, 1351 (1998). 10.1103/PhysRevLett.81.1351
12. M. Hayashi and K. Matsumoto, e-print arXiv:quant-ph/0411073.
13. E. Bagan, M. A. Ballester, R. D. Gill, R. Munoz-Tapia, and O. Romero-Isart, Phys. Rev. Lett. 97, 130501 (2006). 10.1103/PhysRevLett.97.130501
14. M. Guţǎ and J. Kahn, Phys. Rev. A 73, 052108 (2006). 10.1103/PhysRevA.73.052108
15. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Phys. Rev. A 64, 052312 (2001). 10.1103/PhysRevA.64.052312
16. Quantum State Estimation, edited by, M. Paris, and, J. Rehacek, (Springer, Berlin, 2004).
17. K. R. W. Jones, Ann. Phys. (N.Y.) 207, 140 (1991). 10.1016/0003-4916(91) 90182-8
18. E. Bagan, A. Monras, and R. Munoz-Tapia, Phys. Rev. A 71, 062318 (2005). 10.1103/PhysRevA.71.062318
19. R. D. Gill and S. Massar, Phys. Rev. A 61, 042312 (2000). 10.1103/PhysRevA.61.042312
20. J. Rehacek, B.-G. Englert, and D. Kaszlikowski, Phys. Rev. A 70, 052321 (2004). 10.1103/PhysRevA.70.052321
21. A. Roy and A. J. Scott, J. Math. Phys. 48, 072110 (2007). 10.1063/1.2748617
22. A. Fujiwara and H. Nagaoka, Phys. Lett. A 201, 119 (1995). 10.1016/0375-9601(95)00269-9
23. M. Hayashi, in Quantum Communication, Computing and Measurement, edited by, O. Hirota, A. S. Holevo and, C. A. Caves, (Plenum, New York, 1997), pp. 99-108.
24. A. Fujiwara and H. Nagaoka, J. Math. Phys. 40, 4227 (1999). 10.1063/1.532962
25. K. Matsumoto, J. Phys. A 35, 3111 (2002). 10.1088/0305-4470/35/13/307
26. R. Prevedel, P. Walther, F. Tiefenbacher, P. Böhi, R. Kaltenbaek, T. Jennewein, and A. Zeilinger, Nature 445, 65 (2007). 10.1038/nature05346
27. C. A. Fuchs, e-print arXiv:quant-ph/9601020.
28. K. M. R. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, Phys. Rev. Lett. 98, 160501 (2007). 10.1103/PhysRevLett.98.160501
29. C. M. Caves, C. A. Fuchs, and R. Schack, J. Math. Phys. 43, 4537 (2002). 10.1063/1.1494475
30. R. Blume-Kohout and P. Hayden, e-print arXiv:quant-ph/0603116.
31. A. J. Scott, J. Phys. A 39, 13507 (2006). 10.1088/0305-4470/39/43/009
32. K. Zyczkowski and H.-J. Sommers, J. Phys. A 34, 7111 (2001). 10.1088/0305-4470/34/35/335
33. M. J. W. Hall, Phys. Lett. A 242, 123 (1998). 10.1016/S0375-9601(98) 00190-X
34. R. Munoz-Tapia (private communication).
35. M. Mohseni, A. T. Rezakhani, and D. A. Lidar, Phys. Rev. A 77, 032322 (2008). 10.1103/PhysRevA.77.032322
36. M. Hayashi, J. Phys. A 31, 4633 (1998). 10.1088/0305-4470/31/20/006
37. T. Decker, D. Janzing, and T. Beth, Int. J. Quantum Inf. 2, 353 (2004). 10.1142/S0219749904000298
38. B.-G. Englert, T. K. Ming, G. C. Guan, and N. H. Khoon, Laser Phys. 15, 7 (2005).
39. A. Ling, K. P. Soh, A. Lamas-Linares, and C. Kurtsiefer, Phys. Rev. A 74, 022309 (2006). 10.1103/PhysRevA.74.022309
40. A. Ling, A. Lamas-Linares, and C. Kurtsiefer, e-print arXiv:0807.0991.
41. J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, J. Math. Phys. 45, 2171 (2004). 10.1063/1.1737053
42. E. Bagan, M. Baig, and R. Munoz-Tapia, Phys. Rev. Lett. 89, 277904 (2002). 10.1103/PhysRevLett.89.277904
43. E. Bagan, M. Baig, R. Munoz-Tapia, and A. Rodriguez, Phys. Rev. A 69, 010304 (R) (2004). 10.1103/PhysRevA.69.010304
44. J. I. Cirac, L. M. Duan, and P. Zoller, Proceedings of the International School of Physics "Enrico Fermi," Course CXLVIII (OS Press, Amsterdam, 2002), p. 263.
45. J. F. Sturn, SEDUMI: A MATLAB Toolbox for Optimization over Symmetric Cones.
46. A. Hayashi, T. Hashimoto, and M. Horibe, Phys. Rev. A 72, 032325 (2005). 10.1103/PhysRevA.72.032325
47. R. H. Hardin and N. J. A. Sloane, Discrete Comput. Geom. 15, 429 (1996). 10.1007/BF02711518
48. R. B. A. Adamson and A. M. Steinberg, e-print arXiv:0808.0944.
49. I. L. Chuang and M. A. Nielsen, J. Mod. Opt. 44, 2455 (1997).
50. G. M. D'Ariano and P. Lo Presti, Phys. Rev. Lett. 86, 4195 (2001). 10.1103/PhysRevLett.86.4195
51. J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. O'Brien, M. A. Nielsen, and A. G. White, Phys. Rev. Lett. 90, 193601 (2003). 10.1103/PhysRevLett.90.193601