01167nas a2200205   4500000000100000000000100001000000100002008004100003100001800044700001700062700001800079700002200097700002200119700002200141245005200163300001100215490000700226520071400233022001400947       2011                            d1 aCharles Dunkl1 aPiotr Gawron1 aJ.A. Holbrook1 aJaroslaw Miszczak1 aZbigniew Puchała1 aKarol Życzkowski00aNumerical shadow and geometry of quantum states  a3353010 v443 aThe totality of normalised density matrices of order N forms a convex set Q\_N in R^(N^2-1). Working with the flat geometry induced by the Hilbert-Schmidt distance we consider images of orthogonal projections of Q\_N onto a two-plane and show that they are similar to the numerical ranges of matrices of order N. For a matrix A of a order N one defines its numerical shadow as a probability distribution supported on its numerical range W(A), induced by the unitarily invariant Fubini-Study measure on the complex projective manifold CP^(N-1). We define generalized, mixed-states shadows of A and demonstrate their usefulness to analyse the structure of the set of quantum states and unitary dynamics therein.  a1751-8113