On page 1 of this paper it states that the QFI (Quantum Fisher Information) for pure states $\psi$ is $$\mathcal{Q}(\psi) = \sum_{i,j=1}^n\text{Tr}(X_iX_j\psi)-\text{Tr}(X_i \psi)\text{Tr}(X_j \psi)~~~~~~~~~~(3)$$ Further down it states:
It is clear from Eq. (3) that if the generators are chosen from the Pauli group such that there are no stabilizers of the form $\pm X_i$ or $-X_iX_j$, then the QFI of the stabilizer state is equal to the number of stabilizers of the form $X_iX_j$.
How does this conclusion follows from equation (3)? What I get as a start is that if $X_iX_j$ are stabilizers then $$\sum_{i,j=1}^n[\text{Tr}(X_iX_j\psi)-\text{Tr}(X_i \psi)\text{Tr}(X_j \psi)] = \sum_{i,j=1}^n[1-\text{Tr}(X_i \psi)\text{Tr}(X_j \psi)]$$