@article {iitisid_0509,
title = {Numerical shadow and geometry of quantum states},
journal = {J. Phys. A: Math. Theor.},
volume = {44},
number = {33},
year = {2011},
note = {arXiv:1104.2760 IF=1.641(2010);},
pages = {335301},
abstract = {The 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.},
issn = {1751-8113},
author = {Charles F. Dunkl and Piotr Gawron and J.A. Holbrook and J.A. Miszczak and Zbigniew Pucha{\l}a and Karol {\.Z}yczkowski}
}