  In this article, we continue our investigation into the unique continuation
properties of real-valued solutions to elliptic equations in the plane. More
precisely, we make another step towards proving a quantitative version of
Landis' conjecture by establishing unique continuation at infinity estimates
for solutions to equations of the form $- \Delta u + V u = 0$ in
$\mathbb{R}^2$, where $V = V_+ - V_-$, $V_+ \in L^\infty$, and $V_-$ is a
non-trivial function that exhibits exponential decay at infinity. The main tool
in the proof of this theorem is an order of vanishing estimate in combination
with an iteration scheme. To prove the order of vanishing estimate, we
establish a similarity principle for vector-valued Beltrami systems.
