  The measurement range problem, where one cannot determine the data outside
the range of the detector, limits the characterization of entanglement in
high-dimensional quantum systems when employing, among other tools from
information theory, the entropic uncertainty relations. Practically, the
measurement range problem weakens the security of entanglement-based
large-alphabet quantum key distribution (QKD) employing degrees of freedom
including time-frequency or electric field quadrature. We present a modified
entropic uncertainty relation that circumvents the measurement range problem
under certain conditions, and apply it to well-known QKD protocols. For
time-frequency QKD, although our bound is an improvement, we find that high
channel loss poses a problem for its feasibility. In continuous variable QKD,
we find our bound provides a quantitative way to monitor for saturation
attacks.
