  Following the information-based approach to Dirac spinors under a constant
magnetic field, the phase-space representation of symmetric and anti-symmetric
localized Dirac cat states is obtained. The intrinsic entanglement profile
implied by the Dirac Hamiltonian is then investigated so as to shed a light on
quantum states as carriers of qubits correlated by phase-space variables.
Corresponding to the superposition of Gaussian states, cat states exhibit
non-trivial elementary information dynamics which include the interplay between
intrinsic entanglement and quantum superposition as reported by the
corresponding Dirac archetypes. Despite the involved time-evolution as
non-stationary states, the Wigner function constrains the elementary
information quantifiers according to a robust framework which can be
consistently used for quantifying the time-dependent $SU(2) \otimes SU(2)$
(spin projection and intrinsic parity) correlation profile of phase-space
localized Dirac spinor states. Our results show that the Dirac Wigner functions
for cat states -- described in terms of generalized Laguerre polynomials --
exhibit an almost maximized timely persistent mutual information profile which
is engendered by either classical- or quantum-like spin-parity correlations,
depending on the magnetic field intensity.
