Parametrizations of density matrices

Journal of Modern Optics

Volumn 59, Issue 1, 2012, Pages 1-20

  Bruning E ^a   Makela H ^b,c   Messina, A ^c   Petruccione, F ^a  

^a UNIVERSITY OF KWAZULU NATAL   (South Africa)

^b UMEÅ UNIVERSITY   (Sweden)

^c UNIVERSITY OF PALERMO   (Italy)

Author keywords

Bloch vector; density matrix parametrization; finite dimensional density matrix; Jarlskog parametrization; quantum optics (inc. quantum information)

Indexed keywords

BLOCH VECTORS; DENSITY MATRIX; FINITE DIMENSIONAL SYSTEMS; FINITE-DIMENSIONAL DENSITY MATRIX; PARAMETRIZATIONS; POLARIZATION OPERATOR; RECENT PROGRESS; THREE LEVEL SYSTEMS; TIME-DEPENDENT HAMILTONIANS; TWO-QUBIT SYSTEM;

HAMILTONIANS; MATRIX ALGEBRA; QUANTUM OPTICS;

QUANTUM THEORY;

EID: 84856917736     PISSN: 09500340     EISSN: 13623044     Source Type: Journal    
DOI: 10.1080/09500340.2011.632097     Document Type: Review

References (69)

1. Fano, U. Rev. Mod. Phys. 1957, 29, 74-93.
2. Harriman, J.E. Phys. Rev. A 1978, 17, 1249-1256.
3. Kimura, G. Phys. Lett. A 2003, 314, 339-349.
4. Byrd, M.S.; Khaneja, N. Phys. Rev. A 2003, 68, 062322.
5. Elgin, J.N. Phys. Lett. A 1980, 80, 140-142.
6. Hioe, F.T.; Eberly, J.H. Phys. Rev. Lett. 1981, 47, 838-841.
7. Gottlieb, H.P.W. Phys. Rev. A 1982, 26, 3713-3715.
8. Hioe, F.T.; Eberly, J.H. Phys. Rev. A 1982, 25, 2168-2171.
9. Hioe, F.T. Phys. Rev. A 1985, 32, 2824-2836.
10. Fano, U. Rev. Mod. Phys. 1983, 55, 855-874.
11. Schlienz, J.; Mahler, G. Phys. Rev. A 1995, 52, 4396-4404.
12. Aravind, P.K. Am. J. Phys. 1996, 64, 1143-1150.
13. James, D.F.V.; Kwiat, P.G.; Munro, W.J.; White, A.G. Phys. Rev. A 2001, 64, 052312.
14. Abouraddy, A.F.; Sergienko, A.V.; Saleh, B.E.A.; Teich, M.C. Opt. Commun. 2002, 201, 93-98.
15. Jaeger, G.; Teodorescu-Frumosu, M.; Sergienko, A.; Saleh, B.E.A.; Teich, M.C. Phys. Rev. A 2003, 67, 032307.
16. Teodorescu-Frumosu, M.; Jaeger, G. Phys. Rev. A 2003, 67, 052305.
17. Altafini, C. Phys. Rev. A 2004, 69, 012311.
18. Jakob, M.; Bergou, J.A. Phys. Rev. A 2007, 76, 052107.
19. Kryszewski, S.; Zachcial, M. J. Phys. A: Math. Gen. 2006, 39, 5921.
20. Bertlmann, R.A.; Krammer, P. J. Phys. A: Math. Theor. 2008, 41, 235303.
21. Blum, K. Density Matrix Theory and Applications; Plenum Press: New York, 1996.
22. Jarlskog, C. J. Math. Phys. 2005, 46, 103508-103512.
23. Fujii, K.; Funahashi, K.; Kobayashi, T. Int. J. Geom. Methods Mod. Phys. 2006, 3, 269-283.
24. Jarlskog, C. J. Math. Phys. 2006, 47, 013507.
25. Spengler, C.; Huber, M.; Hiesmayr, B.C. J. Phys. A: Math. Theor. 2010, 43, 385306.
26. Horodecki, R.; Horodecki, P.; Horodecki, M.; Horodecki, K. Rev. Mod. Phys. 2009, 81, 865-942.
27. Gühne, O.; Tó th, G. Phys. Rep. 2009, 474, 1-75.
28. Akhtarshenas, S.J. Opt. Spectrosc. 2007, 103, 411-415.
29. Brüning, E.; Chruściń ski, D.; Petruccione, F. Open Syst. Inf. Dyn. 2008, 15, 397-408.
30. Tilma, T.; Sudarshan, E.C.G. J. Phys. A: Math. Gen. 2002, 35, 10467-10501.
31. Tilma, T.; Sudarshan, E.C.G. J. Geom. Phys. 2004, 52, 263-283.
32. Ivanov, P.A.; Kyoseva, E.S.; Vitanov, N.V. Phys. Rev. A 2006, 74, 022323.
33. Ivanov, P.A.; Torosov, B.T.; Vitanov, N.V. Phys. Rev. A 2007, 75, 012323.
34. Ivanov, S.S.; Ivanov, P.A.; Vitanov, N.V. Phys. Rev. A 2008, 78, 030301.
35. Diţa?, P. J. Phys. A: Math. Gen. 2003, 36, 2781-2789.
36. Dita, P. J. Phys. A: Math. Gen. 2005, 38, 2657.
37. Blanchard, P.; Brüning, E. Mathematical Methods in Physics: Distributions, Hilbert Space Operators and Variational Methods. In Progress in Mathematical Physics; Birkhäuser: Boston, MA, 2003.
38. Gilmore, R. Lie Groups, Lie Algebras, and Some of Their Applications; Wiley: New York, 1974.
39. Adelman, M.; Corbett, J.; Hurst, C.A. Found. Phys. 1993, 23, 211-223.
40. Brüning, E.; Petruccione, F. Open Syst. Inf. Dyn. 2008, 15, 109-121.
41. Harriman, J.E. Phys. Rev. A 1978, 17, 1257-1268.
42. Harriman, J.E. Phys. Rev. A 1983, 27, 632-645.
43. Harriman, J.E. Phys. Rev. A 1986, 34, 29-39.
44. Hioe, F.T. Phys. Rev. A 1984, 30, 3097-3106.
45. Oreg, J.; Hazak, G.; Eberly, J.H. Phys. Rev. A 1985, 32, 2776-2783.
46. Pöttinger, J.; Lendi, K. Phys. Rev. A 1985, 31, 1299-1309.
47. Lendi, K. Phys. Rev. A 1986, 33, 3358-3362.
48. Alicki, R.; Lendi, K. Quantum Dynamical Semigroups and Applications; Lecture Notes in Physics 717; Springer: Berlin, Heidelberg, 2007.
49. Lendi, K. Phys. Rev. A 1986, 34, 662-663.
50. Altafini, C. J. Math. Phys. 2003, 44, 2357-2372.
51. Schirmer, S.G.; Zhang, T.; Leahy, J.V. J. Phys. A: Math. Gen. 2004, 37, 1389.
52. Boya, L.J.; Dixit, K. Phys. Rev. A 2008, 78, 042108.
53. Mendaš, I.P. J. Phys. A: Math. Gen. 2006, 39, 11313.
54. Mendaš, I.P. J. Math. Phys. 2008, 49, 092101.
55. Krammer, P. J. Phys. A: Math. Theor. 2009, 42, 065305.
56. Jakó bczyk, L.; Siennicki, M. Phys. Lett. A 2001, 286, 383-390.
57. Schirmer, S.G.; Wang, X. Phys. Rev. A 2010, 81, 062306.
58. Reed, M.; Simon, B. Methods of Modern Mathematical Physics II: Fourier Analysis, Self Adjointness; Academic Press: London, 1975.
59. Dattoli, G.; Gallardo, J.C.; Torre, A. Riv. Nuovo Cimento 1988, 11, 1-79.
60. Kuna, M.; Naudts, J. Solving the von Neumann Equation with Time-dependent Hamiltonian. Part I: Method. 2008, arXiv:math-phys 0805.4487v1 e-Print archive.
61. Pegg, D.T. J. Phys. B: At. Mol. Phys. 1985, 18, 415-421.
62. Peres, A. Phys. Rev. Lett. 1996, 77, 1413-1415.
63. Horodecki, M.; Horodecki, P.; Horodecki, R. Phys. Lett. A 1996, 223, 1-8.
64. Biedenharn, L.C.; Louck, J.D. Angular Momentum in Quantum Physics: Theory and Application; Addison- Wesley: Boston, MA, 1981.
65. Varshalovich, D.A.; Moskalev, A.N.; Khersonskii, V.K. Quantum Theory of Angular Momentum; World Scientific: Singapore, 1988.
66. Fujii, K. Comment on ''A Recursive Parametrisation of Unitary Matrices''. 2005, arXiv:math-phys 0505047v3.
67. Varadarajan, V.S. Lie Groups, Lie Algebras, and Their Representations. Graduate Texts in Mathematics, 2nd ed.; Springer-Verlag: New York, 1984; Vol. 102.
68. Chruściń ski, D.; Kossakowski, A. Phys. Rev. A 2007, 76, 032308.
69. Gurvits, L.; Barnum, H. Phys. Rev. A 2003, 68, 42312.