Hannover 2013 – wissenschaftliches Programm
Q 13.4: Vortrag
Montag, 18. März 2013, 14:45–15:00, E 214
Extremal properties of the variance and the quantum Fisher information — •Géza Tóth1,2,3 and Dénes Petz4 — 1Theoretical Physics, University of the Basque Country UPV/EHU, E-48080 Bilbao, Spain — 2IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain — 3Wigner Research Centre for Physics, H-1525 Budapest, Hungary — 4Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1051 Budapest, Hungary
We show that the variance is its own concave roof. For rank-2 density matrices and operators with zero diagonal elements in the eigenbasis of the density matrix, we show analytically that the quantum Fisher information is 4 times the convex roof of the variance. Strong numerical evidence suggests that the quantum Fisher information is very close to the convex roof even for operators with nonzero diagonal elements or density matrices with a rank larger than 2. Hence, we conjecture that the quantum Fisher information is 4 times the convex roof of the variance even for the general case.