  We use a quantum sensor based on thermal Rydberg atoms to receive data
encoded in electromagnetic fields in the extreme electrically small regime,
with a sensing volume over $10^7$ times smaller than the cube of the electric
field wavelength. We introduce the standard quantum limit for data capacity,
and experimentally observe quantum-limited data reception for bandwidths from
10~kHz up to 30~MHz. In doing this, we provide a useful alternative to
classical communication antennas, which become increasingly ineffective when
the size of the antenna is significantly smaller than the wavelength of the
electromagnetic field.
