  We investigate the properties of the QCD matter across the deconfinement
phase transition. In the scope of the parton-hadron string dynamics (PHSD)
transport approach, we study the strongly interacting matter in equilibrium as
well as the out-of equilibrium dynamics of relativistic heavy-ion collisions.
We present here in particular the results on the electromagnetic radiation,
i.e. photon and dilepton production, in relativistic heavy-ion collisions and
the relevant correlator in equilibrium, i.e. the electric conductivity. By
comparing our calculations for the heavy-ion collisions to the available data,
we determine the relative importance of the various production sources and
address the possible origin of the observed strong elliptic flow $v_2$ of
direct photons.
