  Electrical conductance is quantized in units of $\sigma_{\rm Q}=2e^2/h$ in
ballistic one-dimensional conductors. Similarly, thermal conductance at
temperature $T$ is expected to be limited by the quantum of thermal conductance
of one mode, $G_{\rm Q} = \frac{\pi k_{\rm B}^2}{6\hbar}T$, when physical
dimensions are small in comparison to characteristic wavelength of the
carriers. The relation between $\sigma_{\rm Q}$ and $G_{\rm Q}$ obeys the
Wiedemann-Franz law for ballistic electrons (apart from factor 2 in
$\sigma_{\rm Q}$ due to spin degeneracy), but somewhat amazingly the same
expression of $G_{\rm Q}$ is expected to hold also for phonons and photons, or
any other particles with arbitrary exclusion statistics. The single-mode heat
conductance is particularly relevant in nano-structures, e.g., when studying
heat conduction by phonons in dielectric materials, or cooling of electrons in
metals at very low temperatures. Here we show, based on our experimental
results, that at low temperatures heat is transferred by photon radiation, in
our case along a superconducting line, when electron-phonon as well as normal
electronic heat conduction are frozen out. Thermal conductance is limited by
$G_{\rm Q}$, approaching this value towards low temperatures. Our observation
has implications on, e.g., performance and design of ultra-sensitive bolometers
and electronic micro-refrigerators, whose operation is largely dependent on
weak thermal coupling between the device and its environment.
