  The neutral triple gauge couplings~(nTGCs) provide a unique opportunity to
probe new physics beyond the Standard Model. The nTGCs can be described by an
effective field theory~(EFT), which is valid only under a certain energy scale.
One of the signatures that an EFT is no longer valid is the violation of
unitarity. We study the partial wave unitarity bounds on the coefficients of
nTGCs in the process $e^+e^-\to Z\gamma$. In the experiments, the constraints
obtained should be tighter than the unitarity bounds, otherwise the results are
meaningless, therefore there exists a minimal luminosity for a $e^+e^-$
collider such as the CEPC to study the nTGCs. To derive the minimal luminosity,
the kinematic features and event selection strategy are studied by Monte-Carlo
simulation. Both the processes $e^+e^-\to \ell^+\ell^-\gamma$ and $e^+e^-\to
jj\gamma$ are studied, event selection strategies are discussed. Based on the
statistical significance, the expected constraints in experiments are
estimated. The required luminosities for the experiments to reach the unitarity
bounds are presented.
