  We consider the quantum cat map - a toy model of a quantized chaotic system.
We show that its eigenstates are fully delocalized on $\mathbb{T}^2$ in the
semiclassical limit (or equivalently that each semiclassical measure is fully
supported on $\mathbb{T}^2$). We adapt the proof of a similar result proved for
the eigenstates of $-\Delta_g$ on compact hyperbolic surfaces from
[arXiv:1705.05019], relying on the fractal uncertainty principle in
[arXiv:1612.09040].
