**Abstract**

Recently one has observed that the entanglement between SU(2) x SU(2) internal degrees of freedom of parity and helicity Dirac-like particles corresponding to SU(2) x SU(2) polarized structures can be straightforwardly translated into a useful theoretical tool for obtaining the spin-spin entanglement in the context of enlarged scenarios of nonrelativistic 2D systems, as for instance those for describing single (or even double) layer graphene, or single trapped ions with Dirac bi-spinor mathematical structure.Dirac-like global potentials driven by (pseudo)scalar, (pseudo)vector and tensor interactions may therefore destroy the SU(2) x SU(2) separability and create quantum correlations (as for instance, the entanglement of formation) of controllable systems with enormous physical appeal when mapped onto the bi-spinor structure.Some of ours recent assertive results establishes that the SU(2) x SU(2) group structure of Dirac bi-spinors are are assigned to a Dirac Hamiltonian written in terms of the direct product of two-qubit operators, from which the free particle solutions of the Dirac equation are given in terms of SU(2) x SU(2) parity-spin entangled states.The preliminary purpose of our project is to quantify the role of (pseudo)scalar, (pseudo)vector and tensor interactions in producing/destroying quantum correlations in SU(2) x SU(2) bi-spinor structures.Considering that low-energy excitations of a nonrelativistic electrons in the single layer graphene exhibits a massless Weyl spinor structure often related to 2D Dirac equation solutions supported by a SU(2) structure, the quantum separability of electron-electron or electron-hole describe through such structures can be quantified under different circumstances of interaction.Analogously, noticing that the trapped-ions work as a flexible platform to map several suitable effects in relativistic Dirac quantum mechanics (as for instance, in discussing the planar diffusion and the 2D scattering of the correspondingbi-spinor structures), our final aim consists in applying the framework for quantifying the pertinent quantum correlations related to the trapped-ion physics. (AU)

Scientific publications
(12)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)