TY - JOUR
AU - Charles Dunkl
AU - Piotr Gawron
AU - J.A. Holbrook
AU - Jaroslaw Miszczak
AU - Zbigniew Puchała
AU - Karol Życzkowski
AB - 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.
BT - J. Phys. A: Math. Theor.
LA - eng
M1 - 33
N1 - arXiv:1104.2760 IF=1.641(2010);
N2 - 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.
PY - 2011
EP - 335301
T2 - J. Phys. A: Math. Theor.
TI - Numerical shadow and geometry of quantum states
VL - 44
SN - 1751-8113
ER -