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Original Articles

An LMI description for the cone of Lorentz-positive maps

Pages 551-573 | Received 17 Jan 2006, Accepted 07 Dec 2006, Published online: 09 Oct 2007

References

  • Gurvits , L and Barnum , H . 2003 . Separable balls around the maximally mixed multipartite quantum states. . Physical Review , 68 : 042312
  • Choi , M-D . 1974 . A Schwarz inequality for positive linear maps on C-algebras . Illinois Journal of Mathematics , 18 ( 4 ) : 565 – 574 .
  • Størmer , E . 1963 . Positive linear maps of operator algebras . Acta Mathematica , 110 : 233 – 278 .
  • Terpstra , F . 1939 . Die Darstellung biquadratischer Formen als Summen von Quadraten mit Anwendung auf die Variationsrechnung . Mathematische Annalen , 116 : 166 – 180 .
  • Horodecki , R , Horodecki , P and Horodecki , M . 1996 . Separability of mixed states: necessary and sufficient conditions. . Physics Letters , 223 ( 1 ) : 1 – 8 .
  • Peres , A . 1996 . Separability criterion for density matrices. . Physics Review Letters , 77 : 1413 – 1415 .
  • Ben-Tal , A. and Nemirovski , A . 1998 . Robust convex optimization. . Mathematics of Operations Research , 23 : 769 – 805 .
  • Woronowicz , S . 1976 . Positive maps of low dimensional matrix algebras. . Reports on Mathematical Physics , 10 : 165 – 183 .
  • Sturm , JF and Zhang , S . 2003 . On cones of nonnegative quadratic functions. . Mathematics of Operations Research , 28 ( 2 ) : 246 – 267 .
  • Luo , Z-Q , Sturm , JF and Zhang , S . 2004 . Multivariate nonnegative quadratic mappings. . SIAM Journal of Optimization , 14 ( 4 ) : 1140 – 1162 .
  • Nemirovski , A . 2005 . “ A separation oracle for the cone of Lorentz-positive matrices ” . Georgia Tech School of Industrial and Systems Engineering . private communication
  • Boyd , S , Ghaoui , L , Feron , E and Balakrishnan , V . 1994 . “ Linear matrix inequalities in system and control theory ” . In SIAM Studies in Applied Mathematics
  • Bauschke , HH , Güler , O , Lewis , AS and Sendov , HS . 2001 . Hyperbolic polynomials and convex analysis. . Canadian Journal of Mathematics , 53 ( 3 ) : 470 – 488 .
  • Porteous , I . 1969 . Topological Geometry , New York : van Nostrand .
  • Lounesto , P . 2001 . Clifford Algebras and Spinors , Cambridge : Cambridge University Press .
  • Cartan , E . The Theory of Spinors , New York : Dover .
  • Warner , F . 1983 . Foundations of Differentiable Manifolds and Lie Groups , New York, Berlin, Heidelberg, Tokyo : Springer .
  • Wikipedia . Clifford algebras. http://en.wikipedia.org/wiki/Clifford algebra
  • Dines , LL . 1943 . On linear combinations of quadratic forms. . Bulletin of the American Mathematical Society , 49 : 388 – 393 .
  • Yakubovitch , V . 1970 . Factorization of symmetric matrix polynomials. . Doklady Akademii Nauk SSSR , 194 ( 3 ) : 1261 – 1264 .
  • Gurvits , L . 2003 . Classical deterministic complexity of Edmonds' problem and quantum entanglement. . arXiv quant-ph e-print 0303055
  • Vinberg , EB . 1963 . The theory of convex homogeneous cones. . Transactions of Moscow Mathematical Society , 12 : 340 – 403 .
  • Gurvits , L . 2004 . Revisiting separability of 2 × 2 quantum systems . personal communication

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