For the first time, the possibility of measuring the difference in gravitational potentials and orthometric heights using a quantum level based on the gravitational effect of time dilation using ground communication lines is considered. The duplex mode of measurements using two opposite radio channels is theoretically described. The deceleration effect was experimentally measured using a one-way radio link implemented on a fiber-optic link. For measurements, stationary and relocatable quantum hydrogen clocks with relative instability, respectively, (0.5–0.7)∙10–15 and 1∙10–15 were used. It was found that in the experiment the gravitational redshift of the frequency between the clocks used has two components: the redshift of the clock master oscillator frequency and the classical redshift in the radio channel. Based on the measurement results, the altitude of the relocated quantum hydrogen clock was calculated, which was (–34.0±0.8) m at the actual altitude –34 m.