Reporting about the Wigner formalism for describing Dirac spinor structures through a covariant phase-space formulation, the quantum information quantifiers for purity and mutual information involving spin-parity (discrete) and position-momentum (continuous) degrees of freedom are consistently obtained. For Dirac spinor Wigner operators decomposed into Poincaré classes of $SU(2) \otimes SU(2)$ spinor couplings, a definitive expression for quantum purity is identified in a twofold way: firstly, in terms of phase-space positively defined quantities, and secondly, in terms of the {\em spin-parity traced-out} associated density matrix in the position coordinate representation, both derived from the original Lorentz covariant phase-space Wigner representation. Naturally, such a structure supports the computation of relative (linear) entropies respectively associated to discrete (spin-parity) and continuous (position-momentum) degrees of freedom. The obtained theoretical tools are used for quantifying (relative) purities, mutual information as well as, by means of the quantum concurrence quantifier, the spin-parity quantum entanglement, for a charged fermion trapped by a uniform magnetic field which, by the way, has the phase-space structure completely described in terms of Laguerre polynomials associated to the quantized Landau levels. Our results can be read as the first step in the systematic computation of the elementary information content of Dirac-like systems exhibiting some kind of confining behavior.
Self-Ordered Supersolid in Spinor Condensates with Cavity-Mediated Spin-Momentum-Mixing Interactions
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所、中国科学院理论物理重点实验室）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学、中国科学院拓扑量子计算卓越创新中心）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Multicomponent anyons in one-dimensional optical lattices
Rice University（莱斯大学）；The University of Oklahoma（俄克拉荷马大学）；Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新研究院）；Research School of Physics, Australian National University（澳大利亚国立大学物理研究学院）
