  Non-Hermitian parity-time ($\mathcal{PT}$) and anti-parity-time
($\mathcal{APT}$)-symmetric systems exhibit novel quantum properties and have
attracted increasing interest. Although many counterintuitive phenomena in
$\mathcal{PT}$- and $\mathcal{APT}$-symmetric systems were previously studied,
coherence flow has been rarely investigated. Here, we experimentally
demonstrate single-qubit coherence flow in $\mathcal{PT}$- and
$\mathcal{APT}$-symmetric systems using an optical setup. In the symmetry
unbroken regime, we observe different periodic oscillations of coherence.
Particularly, we observe two complete coherence backflows in one period in the
$\mathcal{PT}$-symmetric system, while only one backflow in the
$\mathcal{APT}$-symmetric system. Moreover, in the symmetry broken regime, we
observe the phenomenon of stable value of coherence flow. We derive the
analytic proofs of these phenomena and show that most experimental data agree
with theoretical results within one standard deviation. This work opens avenues
for future study on the dynamics of coherence in $\mathcal{PT}$- and
$\mathcal{APT}$-symmetric systems.
