  A common feature of collapse models and an expected signature of the
quantization of gravity at energies well below the Planck scale is the
deviation from ordinary quantum-mechanical behavior. Here, we analyze the
general consequences of such modifications from the point of view of quantum
information theory and we anticipate applications to different quantum systems.
We show that quantum systems undergo corrections to the quantum speed limit
which, in turn, imply the modification of the Heisenberg limit for parameter
estimation. Our results hold for a wide class of scenarios beyond ordinary
quantum mechanics. For some nonlocal models inspired by quantum gravity, the
bounds are found to oscillate in time, an effect that could be tested in future
high-precision quantum experiments.
