  We discuss how to calculate genuine multipartite quantum and classical
correlations in symmetric, spatially invariant, mixed $n$-qubit density
matrices. We show that the existence of symmetries greatly reduces the amount
of free parameters to be optimized in order to find the optimal measurement
that minimizes the conditional entropy in the discord calculation. We apply
this approach to the states exhibited dynamically during a thermodynamic
protocol to extract maximum work. We also apply the symmetry criterion to a
wide class of physically relevant cases of spatially homogeneous noise over
multipartite entangled states. Exploiting symmetries we are able to calculate
the nonlocal and genuine quantum features of these states and note some
interesting properties.
