  The conditional mutual information (CMI) $\mathcal{I}(A\! : \! C|B)$
quantifies the amount of correlations shared between $A$ and $C$ \emph{given}
$B$. It therefore functions as a more general quantifier of bipartite
correlations in multipartite scenarios, playing an important role in the theory
of quantum Markov chains. In this paper we carry out a detailed study on the
behavior of the CMI in non-equilibrium steady-states (NESS) of a quantum chain
placed between two baths at different temperatures. These results are used to
shed light on the mechanisms behind ballistic and diffusive transport regimes
and how they affect correlations between different parts of a chain. We carry
our study for the specific case of a 1D bosonic chain subject to local Lindblad
dissipators at the boundaries. In addition, the chain is also subject to
self-consistent reservoirs at each site, which are used to tune the transport
between ballistic and diffusive. As a result, we find that the CMI is
independent of the chain size $L$ in the ballistic regime, but decays
algebraically with $L$ in the diffusive case. Finally, we also show how this
scaling can be used to discuss the notion of local thermalization in
non-equilibrium steady-states.
