  We prove that if a solution of the discrete time-dependent Schr\"odinger
equation with bounded real potential decays fast at two distinct times then the
solution is trivial. For the free Shr\"odinger operator and for operators with
compactly supported time-independent potentials a sharp analog of the Hardy
uncertainty principle is obtained, using an argument based on the theory of
entire functions. Logarithmic convexity of weighted norms is employed in the
case of general real-valued time-dependent bounded potentials. In the latter
case the result is not optimal.
