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A description of the effects of the local noise on the quantum entanglementconstraining the internal degrees of freedom of Dirac bi-spinor structuresdriven by arbitrary Poincar\'{e} invariant potentials is proposed. Given thatthe Dirac equation dynamics including external potentials can be simulated by asuitable four level trapped ion setup, quantum entanglement of two-qubit ionicstates with quantum numbers related to the total angular momentum and to itsprojection onto the direction of the external magnetic field (used for lift theions degeneracy), are recovered by means of a suitable ansatz. This formalismallows the inclusion of noise effects, which leads to disentanglement in thefour level trapped ion quantum system. Our results indicate the role ofinteractions in bi-spinor entanglement, as well as the description ofdisentanglement in ionic states under local noises. For a state preparedinitially in one of the ionic levels, local noise induces entanglement suddendeath followed by sudden revivals driven by the noiseless dynamics of thestate. Residual quantum correlations are observed in the intervals where suchstate is separable. Schr\"odinger cat and Werner states partially loose theirinitial entanglement content due to the interaction with the noisy environmentbut presenting entanglement oscillations without sudden death. Because Diracequation describes low energy excitations of mono layer and bi-layer graphene,the formalism can also be applied to compute, for instance, electron-hole orelectron/electron entanglement in various circumstances.

Dirac bi-spinor entanglement under local noise and its simulation by Jaynes-Cummings interactions