  A description of the effects of the local noise on the quantum entanglement
constraining the internal degrees of freedom of Dirac bi-spinor structures
driven by arbitrary Poincar\'{e} invariant potentials is proposed. Given that
the Dirac equation dynamics including external potentials can be simulated by a
suitable four level trapped ion setup, quantum entanglement of two-qubit ionic
states with quantum numbers related to the total angular momentum and to its
projection onto the direction of the external magnetic field (used for lift the
ions degeneracy), are recovered by means of a suitable ansatz. This formalism
allows the inclusion of noise effects, which leads to disentanglement in the
four level trapped ion quantum system. Our results indicate the role of
interactions in bi-spinor entanglement, as well as the description of
disentanglement in ionic states under local noises. For a state prepared
initially in one of the ionic levels, local noise induces entanglement sudden
death followed by sudden revivals driven by the noiseless dynamics of the
state. Residual quantum correlations are observed in the intervals where such
state is separable. Schr\"odinger cat and Werner states partially loose their
initial entanglement content due to the interaction with the noisy environment
but presenting entanglement oscillations without sudden death. Because Dirac
equation describes low energy excitations of mono layer and bi-layer graphene,
the formalism can also be applied to compute, for instance, electron-hole or
electron/electron entanglement in various circumstances.
