Variational quantum tomography with incomplete information by means of semidefinite programs

International Journal of Modern Physics C

Volumn 22, Issue 12, 2011, Pages 1361-1372

  MacIel, Thiago O ^a   Cesário, André T ^a   Vianna, Reinaldo O ^a  

^a FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

Author keywords

compressed sensing approaches; Quantum tomography; semidefinite programs

Indexed keywords

EID: 84855689012     PISSN: 01291831     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129183111016981     Document Type: Article

References (23)

1. M. Paris and J. Rehacek (eds.), Quantum State Estimation, Lect. Notes Phys., Vol. 649 (Springer, Berlin, Heidelberg, 2004), DOI 10.1007/b98673.
2. Z. Hradil, J. Rehacek, J. Fiurasek and M. Jezek, Maximum-likelihood methods in quantum mechanics, in Quantum State Estimation, M. Paris and J. Rehacek (eds.), Lect. Notes Phys., Vol. 649 (Springer, Berlin, Heidelberg, 2004), DOI 10.1007/b98673, p. 59.
3. G. M. D'Ariano, D. F. Magnani and P. Perinotti, Phys. Lett. A 373, 111 (2009).
4. G. M. D'Ariano and P. Perinotti, Phys. Rev. Lett. 98, 020403 (2007).
5. J. Rehacek, Z. Hradil, E. Knill and A. I. Lvovsky, Phys. Rev. A 75, 042108 (2007).
6. R. Horodecki, M. Horodecki and P. Horodecki, Phys. Rev. A 59, 1799 (1999).
7. F. G. S. L. Brandão and R. O. Vianna, Phys. Rev. Lett. 93, 220503 (2004).
8. F. G. S. L. Brandão and R. O. Vianna, Int. J. Quantum Inf. 4, 331 (2006).
9. F. G. S. L. Brandão and R. O. Vianna, Phys. Rev. A 70, 062309 (2004).
10. T. O. Maciel and R. O. Vianna, Phys. Rev. A 80, 032325 (2009).
11. H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür and R. Blatt, Nature 438, 643 (2005).
12. E. T. Jaynes, Phys. Rev. 106, 620 (1957).
13. V. Buzek, Quantum tomography from incomplete data via MaxEnt principle, in Quantum State Estimation, M. Paris and J. Rehacek (eds.), Lect. Notes Phys., Vol. 649 (Springer, Berlin, Heidelberg, 2004), DOI 10.1007/b98673, p. 189.
14. S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge Univ. Press, Cambridge, 2000).
15. J. F. Sturm, Optim. Methods Softw. 11, 625 (1999); SEDUMI: http://fewcal.kub.nl/ sturm/softwares/sedumi.html.
16. J. Löfberg, YALMIP: A toolbox for modeling and optimization in MATLAB, in Proc. CACSD Conf., Taipei, Taiwan, 2004. (Unpublished) http://control.ee.ethz.ch/-joloef/yalmip.php.
17. D. Gross, Y. Liu, T. Flammia, T. S. Becker and J. Eisert, Phys. Rev. Lett. 105, 150401 (2010).
18. G. Lima, E. S. G-omez, A. Vargas, R. O. Vianna and C. Saavedra, Phys. Rev. A 82, 012302 (2010).
19. R. F. Werner, Phys. Rev. A 40, 4277 (1989).
20. I. D. Ivanovic, J. Phys. A: Math. Gen. 14, 3241 (1981).
21. W. K. Wootters and B. D. Fields, Ann. Phys. 191, 363 (1989).
22. J. K. Renes, R. Blume-Kohout, A. J. Scott and C. M. Caves, J. Math. Phys. 45, 2171 (2004).
23. T. O. Maciel and R. O. Vianna, Optimal estimation of quantum processes using incomplete information: Variational quantum process tomography, arXiv:1007.2395.