  We identify a class of quantum states, each consisting of a microscopic and a
macroscopic section, that are effectively decoherence-free when each particle
is locally passed through a quantum channel. In particular, and in contrast to
other macroscopic quantum states like the Greenberger-Horne-Zeilinger state,
the content of entanglement and other quantum correlations in the microscopic
to macroscopic partition of this class of states is independent of the number
of particles in their macroscopic sectors, when all the particles suffer
passage through local amplitude and phase damping channels. Decay of quantum
correlations -- entanglement as well as quantum discord -- of this class of
states in the microscopic to macroscopic partition is also much lower in the
case of all the local quantum channels, as compared to the other macroscopic
superposition states. The macroscopic sections of the states are formed, in
each case, by using a Dicke state and an orthogonal product state, which are
macroscopically distinct in terms of markedly different amounts of violation of
Bell inequality.
