Ladder LC Filter - why are they minimum phase?
If we model a lossless transmission line as a pure time delay, its transfer function would be \$\small G(s)=e^{-sT}\$. To be minimum phase, the inverse would need to be causal, and \$e^{sT}\$ is non-causal, hence the transmission line is non-minimum phase with this model.

If we model the line by an L-C ladder, then we are doing something akin to using a Pade approximant, and we can make as accurate a model as we wish by increasing the order of the model.

In its simplest form for the problem to hand, the (0, 2) Pade approximant of \$\small e^{-sT}\$ is:
$$ \small G(s)=e^{-sT}\rightarrow \small\frac{2}{2+2Ts+T^2\small  s^2}$$

which is causal and minimum phase as the inverse can be realised by a differentiator and a double-differentiator.

This compares, for example, with a single-stage L-C ladder TF model: $$\small G(s)=\frac{1}{1+(LC)s^2}$$