  We study two types of unique continuation properties for the higher order
Schr\"{o}dinger equation with potential $$
i\partial_tu=(-\Delta_x)^mu+V(t,x)u,\quad(t,x)\in\mathbb{R}^{1+n},\,2\leq
m\in\mathbb{N}_+. $$ The first one says if $u$ has certain exponential decay at
two times, then $u\equiv0$, and this result is sharp by constructing critical
non-trivial solutions. The second one says if $u\equiv0$ in an arbitrary
half-space of $\mathbb{R}^{1+n}$, then $u\equiv0$ identically. The uniqueness
theorems are given when $n=1$, but we also prove partial results when
$n\in\mathbb{N}_+$ for their own interests. Possibility or obstacles to proving
these unique continuation properties in higher spatial dimensions are also
discussed.
