  We prove unique continuation properties for linear variable coefficient
Schr\"odinger equations with bounded real potentials. Under certain smallness
conditions on the leading coefficients, we prove that solutions decaying faster
than any cubic exponential rate at two different times must be identically
zero. Assuming a transversally anisotropic type condition, we recover the sharp
Gaussian (quadratic exponential) rate in the series of works by
Escauriaza-Kenig-Ponce-Vega [14, 17, 18].
