@article{bibcite_14623,
  author = {Charles Dunkl and Piotr Gawron and J.A. Holbrook and Jaroslaw Miszczak and Zbigniew Pucha{\l}a and Karol {\.Z}yczkowski},
  title = {Numerical shadow and geometry of quantum states},
  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.},
  year = {2011},
  journal = {J. Phys. A: Math. Theor.},
  volume = {44},
  number = {33},
  pages = {335301},
  issn = {1751-8113},
  note = {arXiv:1104.2760 IF=1.641(2010);},
  language = {eng},
}