Tensor products of convex sets and the volume of separable states on N qudits

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 73, Issue 2, 2006, Pages

  Aubrun, Guillaume ^a   Szarek, Stanisław J ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ELEMENTARY PARTICLES; PROBABILITY; QUANTUM THEORY; TENSORS;

BANACH SPACES; CLASSICAL CONVEXITY; CONVEX SETS;

SET THEORY;

EID: 33144464230     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.73.022109     Document Type: Article

References (27)

1. R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.4277 40, 4277 (1989).
2. K. Åyczkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.883 58, 883 (1998).
3. M. Horodecki, P. Horodecki, and R. Horodecki, in Quantum Information, edited by, G. Alber, Springer Tracts in Modern Physics Vol. 173 (Springer, Berlin, 2001), p. 151.
4. S. J. Szarek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.032304 72, 032304 (2005).
5. L. Gurvits and H. Barnum, quant-ph/0409095 (unpublished).
6. A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413 77, 1413 (1996).
7. K. Åyczkowski and H.-J. Sommers, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/39/310 36, 10115 (2003).
8. S. J. Szarek and N. Tomczak-Jaegermann, Compos. Math. CMPMAF 0010-437X 40, 367 (1980).
9. S. L. Braunstein and C. M. Caves, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.3439 72, 3439 (1994).
10. P. Rungta, in Directions in Quantum Optics, Vol. 561 of Lecture Notes in Physics (Springer, Berlin, 2001), p. 149.
11. L. Gurvits and H. Barnum, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.042312 68, 042312 (2003).
12. L. Gurvits and H. Barnum, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.062311 66, 062311 (2002).
13. M. Talagrand, Spin Glasses: A Challenge for Mathematicians (Springer-Verlag, Berlin, 2003).
14. X. Fernique, Fonctions Aléatoires Gaussiennes, Vecteurs Aléatoires Gaussiens (Université de Montré al, Montreal, 1997).
15. R. J. Gardner, Bull., New Ser., Am. Math. Soc. 0273-0979 39, 355 (2002).
16. C. A. Rogers and G. C. Shephard, J. Lond. Math. Soc. JLMSAK 0024-6107 33, 270 (1958).
17. K. Ball, In Flavors of Geometry, Vol. 31 of Math. Sci. Res. Inst. Publ. (Cambridge University Press, Cambridge, 1997).
18. G. Svetlichny, URL http://www.mat.puc-rio.br/svetlich/files/statsci.pdf
19. A. Defant and K. Floret, Tensor Norms and Operator Ideals (North-Holland, Amsterdam, 1993).
20. Y. Luke, Math. Balkanica 2, 118 (1972).
21. K. R. Davidson and S. J. Szarek, in Handbook of the Geometry of Banach Spaces, edited by, W. B. Johnson, and, J. Lindenstrauss, (North-Holland, Amsterdam, 2001), Vol. 1, pp. 317-366
22. (North-Holland, Amsterdam, 2003), Vol. 2, pp. 1819-1820.
23. G. Pisier, The Volume of Convex Bodies and Banach Space Geometry (Cambridge University, Cambridge, U.K., 1989).
24. G. Aubrun, S. J. Szarek, and E. Werner (unpublished).
25. N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals (Longman Scientific & Technical, Harlow, 1989).
26. F. Barthe, Invent. Math. INVMBH 0020-9910 134, 335 (1998).
27. V. D. Milman and A. Pajor, Adv. Math. ADMTA4 0001-8708 152, 314 (2002).