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For the first time, the possibility of measuring the difference in gravitational potentials and orthometric heights by 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 dilation effect was experimentally measured using a one-way radio communication line implemented based on a fiber-optic link. For measurements, stationary and mobile (transportable) quantum hydrogen clocks were used with relative instabilities of (0.5-0.7)×10-15 and 1×10-15, respectively. It was found that in the experiment, the gravitational redshift of the frequency between the utilized clocks has two components: the redshift of the master oscillator frequency and the classical redshift in the radio channel. Based on the measurement results, the displacement height of the transportable quantum hydrogen clock was calculated to be (–34.0 ± 0.8) m, while the actual height was –34 m. [ABSTRACT FROM AUTHOR]