Hilbert-Schmidt volume of the set of mixed quantum states

Journal of Physics A: Mathematical and General

Volumn 36, Issue 39, 2003, Pages 10115-10130

  Zyczkowski, Karol ^a,b   Sommers, Hans Jürgen ^c  

^a JAGIELLONIAN UNIVERSITY   (Poland)

^b CENTER FOR THEORETICAL PHYSICS   (Poland)

^c UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142198849     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/39/310     Document Type: Article

References (38)

1. Bloore F J 1976 J. Phys. A: Math. Gen. 9 2059
2. Harriman 1978 Phys. Rev. A 17 1249
3. Adelman M, Corbett J V and Hurst C A 1993 Found. Phys. 23 211
4. Życzkowski K, Horodecki P, Sanpera A and Lewenstein M 1998 Phys. Rev. A 58 833
5. Życzkowski K 1999 Phys. Rev. A 60 3496
6. Życzkowski K and Sommers H-J 2001 J. Phys. A: Math. Gen. 34 7111
7. Życzkowski K and Slomczyński W 2001 J. Phys. A: Math. Gen. 34 6689
8. Petz D and Sudar C 1996 J. Math. Phys. 37 2662
9. Hioe F T and Eberly J H 1981 Phys. Rev. Lett. 47 838
10. Rungta P, Munro W J, Nemoto K, Deuar P, Milburn G J and Caves C M 2000 Preprint quant-ph/0001075
11. Arvind, Mallesh K S and Mukunda N 1997 J. Phys. A: Math. Gen. 30 2417
12. Macfarlane A J 1968 Commun. Math. Phys. 11 91
13. Jakóbczyk L and Siennicki M 2001 Phys. Lett. A 286 383
14. Kimura G 2003 The Bloch vector for N-level systems Preprint quant-ph/0301152
15. Hua L K 1963 Harmonic Analysis of Functions of Several Variables in the Classical Domains (Providence, RI: American Mathematical Society) (Chinese original 1958; Russian translation, Moskva 1959)
16. Marinov M S 1981 J. Phys. A: Math. Gen. 14 543
17. Tung W-K 1985 Group Theory in Physics (Singapore: World Scientific)
18. Fuiji K 2002 J. Appl. Math. 2 371
19. Tilma T, Byrd M and Sudarshan E C G 2002 J. Phys. A: Math. Gen. 35 10445
20. Boya L J, Sudarshan E C G and Tilma T 2002 Preprint math-ph/0210033
21. Tilma T and Sudarshan E C G 2002 Generalized Euler angle parameterization for U(N) with applications to SU(N) coset volume measures Preprint math-ph/0210057
22. Caves C 2002 Measures and volumes for spheres, the probability simplex, projective Hubert space and density operators Unpublished notes (webpage: http://info.phys.unm.edu/caves/reports/reports.html)
23. Slater P B 1999 J. Phys. A: Math. Gen. 32 5261
24. Spanier J and Oldham K B 1987 An Atlas of Functions (Washington, DC: Hemisphere)
25. Tucci R R 2002 All moments of the uniform ensemble of quantum density matrices Preprint quant-ph/0206193
26. Hall M J W 1998 Phys. Lett. A 242 123
27. Braunstein S L 1996 Phys. Lett. A 219 169
28. Caves C M, Fuchs C A and Rungta P 2001 Found. Phys. Lett. 14 199
29. Mehta M L 1991 Random Matrices 2nd edn (New York: Academic)
30. Slater PB 2000 Eur. Phys. J. B 17 471
31. Slater P B 2002 Quantum Int. Proc. 1 397
32. Slater P B 2003 Preprint quant-ph/0306132
33. Sommers H-J and Zyczkowski K 2003 Bures measure of the set of mixed quantum states J. Phys. A: Math. Gen. 36 10083
34. Byrd M S and Slater P B 2001 Phys. Lett. A 283 152
35. Bures D J C 1969 Trans. Am. Math. Soc. 135 199
36. Uhlmann A 1976 Rep. Math. Phys. 9 273
37. Boya L J 1991 Rep. Math. Phys. 30 149
38. Byrd M 1998 J. Math. Phys. 39 6125