  Bipartite entanglement entropy of a segment with the length $l$ in $1+1$
dimensional conformal field theories (CFT) follows the formula
$S=\frac{c}{3}\ln l+\gamma$, where $c$ is the central charge of the CFT and
$\gamma$ is a cut-off dependent constant which diverges in the absence of an
ultraviolet cutoff. According to this formula, systems with larger central
charges have {\it{more}} bipartite entanglement entropy. Using quantum Fisher
information (QFI), we argue that systems with bigger central charges not only
have larger bipartite entanglement entropy but also have more multipartite
entanglement content. In particular, we argue that since systems with smaller
{\it{smallest scaling dimension}} have bigger QFI, the multipartite
entanglement content of a CFT is dependent on the value of the smallest scaling
dimension present in the spectrum of the system. We show that our argument
seems to be consistent with some of the existing results regarding the von
Neumann entropy, negativity, and localizable entanglement in $1+1$ dimensions.
Furthermore, we also argue that the QFI decays under renormalization group (RG)
flow between two unitary CFTs. Finally, we also comment on the non-conformal
but scale invariant systems.
