  We study the non-equilibrium dynamics and transport of a PT-symmetric
Luttinger liquid (LL) after an interaction quench. The system is prepared in
domain wall initial state. After a quantum quench to spatially homogeneous,
PT-symmetric LL, the domain wall develops into a flat central region that
spreads out ballistically faster than the conventional Lieb-Robinson maximal
speed. By evaluating the current inside the regular lightcone, we find a
universal conductance $e^2/h$, insensitive to the strength of the PT-symmetric
interaction. On the other hand, by repeating the very same time evolution with
a hermitian LL Hamiltonian, the conductance is heavily renormalized by the
hermitian interaction as $e^2/hK$ with $K$ the LL parameter. Our analytical
results are tested numerically, confirming the universality of the conductance
in the non-hermitian realm.
