1109.2831 (Geza Toth et al.)

Extremal properties of the variance and the quantum Fisher information    [PDF]

Geza Toth, Denes Petz

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 the convex roof of the variance. Numerical evidence suggests that the quantum Fisher information is very close to the convex roof even for operators with a nonzero diagonal element or density matrices with a rank larger than 2.

View original: http://arxiv.org/abs/1109.2831