Error probability analysis in quantum tomography: A tool for evaluating experiments

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 83, Issue 1, 2011, Pages

  Sugiyama, Takanori ^a   Turner, Peter S ^a   Murao, Mio ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR PROBABILITIES; ERROR PROBABILITY ANALYSIS; EXPLICIT RATE; IDENTIFIABILITY; LARGE DEVIATIONS; MAXIMUM LIKELIHOOD ESTIMATOR; QUANTUM TOMOGRAPHY; RISK FUNCTION; STATE TOMOGRAPHY; TOMOGRAPHIC;

EXPERIMENTS; MAXIMUM LIKELIHOOD ESTIMATION; QUANTUM THEORY; TOMOGRAPHY;

PROBABILITY;

EID: 78751563470     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.83.012105     Document Type: Article

References (43)

1. Elements of Quantum Information, edited by, W. P. Schleich, and, H. Walther, (Wiley-VCH, Weinheim, 2007).
2. Quantum State Estimation, edited by, M. Paris, and, J. Rehácek,, Lecture Notes in Physics (Springer, Berlin, 2004).
3. C. R. Rao, Linear Statistical Inference and Its Applications (Wiley, New York, 1973).
4. R. D. Gill and S. Massar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.042312 61, 042312 (2000).
5. J. Rehácek, B.-G. Englert, and D. Kaszlikowski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.052321 70, 052321 (2004). (Pubitemid 40073088)
6. E. Bagan, M. A. Ballester, R. D. Gill, A. Monras, and R. Muñoz-Tapia, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.032301 73, 032301 (2006). (Pubitemid 43327435)
7. J. Nunn, B. J. Smith, G. Puentes, and I. A. Walmsley, e-print arXiv: 0911.4310/quant-ph.
8. R. R. Bahadur, J. C. Gupta, and S. L. Zabell, in Asymptotic Theory of Statistical Tests and Estimates (Academic, New York, 1980), pp. 33-64.
9. X. Shen, Statistica Sinica 11, 479 (2001).
10. R. R. Bahadur, Sankhyā 22, 229 (1960).
11. R. R. Bahadur, Ann. Math. Stat. AASTAD 0003-4851 10.1214/aoms/1177698949 38, 303 (1967).
12. M. Hayashi, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/36/302 35, 7689 (2002). (Pubitemid 37049266)
13. M. Hayashi and K. Matsumoto, IEICE Trans. A 83, 629 (2000) (in Japanese).
14. I. N. Sanov, Mat. Sb. 42, 11 (1957)
15. I. N. Sanov, [Sel. Transl. Math. Stat. Prob. I, 213 (1961)].
16. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, 2nd ed. (Springer, New York, 1998).
17. G. M. D'Ariano and P. L. Presti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.4195 86, 4195 (2001). (Pubitemid 32469518)
18. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.1244 70, 1244 (1993). (Pubitemid 23667281)
19. Z. Hradil, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.55.R1561 55, R1561 (1997).
20. K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.010304 61, 010304 (R) (1999).
21. J. F. Poyatos, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.390 78, 390 (1997).
22. I. L. Chuang and M. A. Nielsen, J. Mod. Opt. 44, 2455 (1997).
23. V. Buzek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.1723 58, 1723 (1998).
24. J. Fiurasek and Z. Hradil, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.020101 63, 020101 (R) (2001).
25. M. F. Sacchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.054104 63, 054104 (2001).
26. A. Luis and L. L. Sanchez-Sato, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.3573 83, 3573 (1999).
27. J. Fiurasek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.024102 64, 024102 (2001).
28. G. Kimura, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(03)00941-1 314, 339 (2003).
29. M. S. Byrd and N. Khaneja, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.062322 68, 062322 (2003).
30. E. Prugovecki, Int. J. Theor. Phys. IJTPBM 0020-7748 10.1007/BF01807146 16, 321 (1977).
31. G. A. V. Buzek, R. Derka, and P. L. Knight, Ann. Phys. APNYA6 0003-4916 10.1006/aphy.1998.5802 266, 454 (1998). (Pubitemid 128347615)
32. R. Schack, T. A. Brum, and C. M. Caves, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.014305 64, 014305 (2001).
33. C. A. Fuchs, R. Schack, and P. F. Scudo, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.062305 69, 062305 (2004).
34. V. Buzek and G. Drobny, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500340008232199 47, 2823 (2000).
35. R. L. Kosut, e-print arXiv: 0812.4323 [quant-ph].
36. A. Wald, Ann. Math. Stat. AASTAD 0003-4851 10.1214/aoms/1177729952 20, 595 (1949).
37. A. L. Rukhin, Ann. Statist. ASTSC7 0090-5364 10.1214/aos/1176346070 11, 202 (1983).
38. E. Bagan, M. A. Ballester, R. D. Gill, R. M. Tapia, and O. Romero-Isart, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.130501 97, 130501 (2006). (Pubitemid 44455060)
39. M. Akahara and K. Takeuchi, Non-regular Statistical Estimation (Springer, New York, 1995).
40. C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, New York, 1976).
41. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, New York, 1982).
42. Asymptotic Theory of Quantum Statistical Inference, edited by, M. Hayashi, (World Scientific, Singapore, 2005).
43. A. D. Kester and W. C. M. Kallenberg, Ann. Statist. ASTSC7 0090-5364 10.1214/aos/1176349944 14, 648 (1986).