Quantum Fisher information Matrix

${\mathcal{F}}_{ab}:=\frac{1}{2}\mathrm{Tr}[\rho \{L_a,L_b\}]$ where:

• $\mathrm{Tr}$ is the Trace Operator
• $\{A,B\}:=AB+BA$ is the anti-commutator.
• $\rho$ is a Density Operator, described through set of parameters $\overrightarrow{x}=(x_1,x_2,\dots ,x_k)$, so that $\rho =\rho \left(\overrightarrow{x}\right)$.
• $L_a$ and $L_b$ are the Symmetric Logarithmic derivative, satisfying the equation ${\partial }_a\rho :=\frac{1}{2}(\rho L_a+L_a\rho )$.