Qubit-qutrit separability-probability ratios

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 71, Issue 5, 2005, Pages

  Slater, Paul B ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PROBABILITY RATIOS; QUBIT-QUTRIT SEPARABILITY;

COMPUTATIONAL METHODS; MATRIX ALGEBRA;

PROBABILISTIC LOGICS;

EID: 26944454042     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.71.052319     Document Type: Article

References (72)

1. K. Życzkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.883 58, 883 (1998).
2. K. Życzkowski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60. 3496 60, 3496 (1999).
3. P. B. Slater, J. Geom. Phys. JGPHE5 0393-0440 10.1016/j.geomphys.2004.04. 011 53, 74 (2005).
4. P. B. Slater, J. Phys. A JPHAC5 0305-4470 32, 5261 (1999).
5. P. B. Slater, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510070126 17, 471 (2000).
6. P. B. Slater, J. Opt. B: Quantum Semiclassical Opt. JOBOFD 1464-4266 10.1088/1464-4266/5/6/018 5, S651 (2003).
7. P. B. Slater, e-print quant-ph/0408157.
8. P. B. Slater, e-print quant-ph/0405114.
9. L. Gurvits and H. Barnum, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.062311 66, 062311 (2002).
10. L. Gurvits and H. Barnum, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.042312 68, 042312 (2003).
11. L. Gurvits and H. Barnum, e-print quant-ph/0409095.
12. S. Szarek, e-print quant-ph/0310061.
13. P. B. Slater, Quantum Inf. Process. QIPUAT 1570-0755 10.1023/A: 1023421914825 1, 397 (2002).
14. R. Clifton, H. Halvorson, and A. Kent, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.042101 61, 042101 (2000).
15. H.-J. Sommers and K. Życzkowski, J. Phys. A JPHAC5 0305-4470 36, 10083 (2003).
16. K. Życzkowski and H.-J. Sommers, J. Phys. A JPHAC5 0305-4470 36, 10115 (2003).
17. H.-J. Sommers and K. Życzkowski, J. Phys. A JPHAC5 0305-4470 37, 8457 (2004).
18. M. Hübner, Phys. Lett. A PYLAAG 0375-9601 63A, 239 (1992).
19. M. Hübner, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(93) 90668-P 179, 226 (1993).
20. J. Dittmann, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/32/14/007 32, 2663 (1999).
21. J. Dittmann, J. Geom. Phys. JGPHE5 0393-0440 10.1016/S0393-0440(98)00068- 0 31, 16 (1999).
22. D. Petz and C. Sudár, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.531535 37, 2662 (1996).
23. E. Witten, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01217730 121, 351 (1989).
24. R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.4277 40, 4277 (1989).
25. H. Hasegawa, Rep. Math. Phys. RMHPBE 0034-4877 39, 49 (1997).
26. D. Petz, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.530611 35, 780 (1994).
27. P. W. Michor, D. Petz, and A. Andai, Infinite Dimen. Anal., Quantum Probab., Relat. Top. 0219-0257 10.1016/S0219-0257(00)00014-5 3, 199 (2002).
28. M. R. Grasselli and R. F. Streater, Infinite Dimen. Anal., Quantum Probab., Relat. Top. 0219-0257 10.1142/S0219025701000462 4, 173 (2001).
29. P. Gibilisco and T. Isola, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1598279 44, 3752 (2003).
30. E. Wigner and M. Yanase, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 49, 910 (1963).
31. S. Luo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.180403 91, 180403 (2003).
32. S. Luo, Proc. Am. Math. Soc. PAMYAR 0002-9939 10.1090/S0002-9939-03- 07175-2 132, 885 (2004).
33. C. Krattenthaler and P. B. Slater, IEEE Trans. Inf. Theory IETTAW 0018-9448 10.1109/18.841164 46, 801 (2000).
34. P. B. Slater, J. Phys. A JPHAC5 0305-4470 34, 7029 (2001).
35. H. P. Yuen and M. Lax, IEEE Trans. Inf. Theory IETTAW 0018-9448 10.1109/TIT.1973.1055103 19, 740 (1973).
36. D. Petz, Linear Algebr. Appl. LAAPAW 0024-3795 10.1016/0024-3795(94) 00211-8 244, 81 (1996).
37. M. Ozawa, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00171-7 268, 158 (2000).
38. K. Życzkowski and H.-J. Sommers, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.032313 71, 032313 (2005).
39. A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413 77, 1413 (1996).
40. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(96)00706-2 223, 1 (1996).
41. A. Sanpera, R. Tarrach, and G. Vidal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.826 58, 826 (1998).
42. F. Verstraete, K. Audenaert, J. Dehaene, and B. D. Moor, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/47/329 34, 10327 (2001).
43. P. Zanardi, D. A. Lidar, and S. Lloyd, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.060402 92, 060402 (2004).
44. P. Caban, K. Podlaski, J. Riembieliński, K. A. Smoliński, and Z. Walczak, J. Phys. A JPHAC5 0305-4470 38, L79 (2005).
45. H. Faure and S. Tezuka, in Monte Carlo and Quasi-Monte Carlo Methods 2000 (Hong Kong), edited by, K. T. Tang, F. J. Hickernell, and, H. Niederreiter, (Springer, Berlin, 2002), p. 242.
46. G. Akten, Math. Educ. Res 1096-3324 8, 52 (1999).
47. T. Tilma, M. Byrd, and E. C. G. Sudarshan, J. Phys. A JPHAC5 0305-4470 35, 10445 (2002).
48. T. Tilma and E. C. G. Sudarshan, J. Phys. Soc. Jpn. JUPSAU 0031-9015 72, Suppl. C, 181 (2003).
49. G. A. Christos and T. Gherghetta, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.44.898 44, 898 (1991).
50. V. W. de Spinadel, Int. Math. J. 2, 279 (2002).
51. G. Gumbs, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/22/8/012 22, 951 (1989).
52. J. Kappraff, Beyond Measure (World Scientific, River Edge, NJ, 2002).
53. G. Markowsky, Not. Am. Math. Soc. AMNOAN 0002-9920 52, 344 (2005).
54. S. L. Braunstein and C. M. Caves, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.3439 72, 3439 (1994).
55. R. Schack and C. M. Caves, J. Mod. Opt. JMOPEW 0950-0340 10.1080/095003400148286 47, 387 (2000).
56. G. Kimura and A. Kossakowski, e-print quant-ph/0408014.
57. M. S. Byrd and N. Khaneja, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.062322 68, 062322 (2003).
58. G. Kimura, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(03)00941-1 314, 339 (2003).
59. C. Bavard and P. Pansu, Ann. Sci. Ec. Normale Super. 0012-9593 19, 479 (1986).
60. B. H. Bowditch, J. Austral. Math. Soc 1446-7887 55, 23 (1993).
61. R. P. Bambah, V. C. Dumir, and R. J. Hans-Gill, Stud. Sci. Math. Hung. SSMHAX 0081-6906 21, 135 (1986).
62. W. J. Morokoff and R. E. Caflisch, Stud. Sci. Math. Hung. SSMHAX 0081-6906 15, 1251 (1994).
63. M. Shi and J. Du, e-print quant-ph/0103016.
64. M. Gromov, Metric Structures for Riemannian and Non-Riemannian Spaces (Birkhäuser, Boston, 1999).
65. N. Oresme, De proportionibus proportionum and Ad pauca respicientes (University of Wisconsin, Madison, 1996).
66. P. Hayden, D. Leung, P. W. Shor, and A. Winter, Commun. Math. Phys. CMPHAY 0010-3616 250, 371 (2004).
67. K. Życzkowski and W. Słomczyńnski, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/34/311 34, 6689 (2001).
68. O. Rudolph, Lett. Math. Phys. LMPHDY 0377-9017 10.1007/s11005-004-0767-7 70, 57 (2004).
69. R. Lockhart, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.064304 65, 064304 (2002).
70. H. S. Hong and F. J. Hickernell, ACM Trans. Math. Softw. ACMSCU 0098-3500 10.1145/779359.779360 29, 95 (2003).
71. G. Call and D. Velleman, Am. Math. Monthly AMMYAE 100, 372 (1993).
72. H.-J. Sommers and K. Życzkowski, e-print quant-ph/0304041 v3.