Lorentz invariant quantum concurrence for $$\textit{SU}(2) \otimes \textit{SU}(2)$$ spin–parity states

Abstract

The quantum concurrence of $SU(2) \otimes SU(2)$ spin-parity states is shown to be invariant under $SO(1,3)$ Lorentz boosts and $O(3)$ rotations when the density matrices are constructed in consonance with the covariant probabilistic distribution of Dirac massive particles. Similar invariance properties are obtained for the quantum purity and for the trace of unipotent density matrix operators. The reported invariance features -- obtained in the scope of the $SU(2) \otimes SU(2)$ corresponding to just one of the inequivalent representations enclosed by the $SL(2,\mathbb{C})\otimes SL(2,\mathbb{C})$ symmetry -- set a more universal and kinematical-independent meaning for the quantum entanglement encoded in systems containing not only information about spin polarization but also the correlated information about intrinsic parity. Such a covariant framework is used for computing the Lorentz invariant spin-parity entanglement of spinorial particles coupled to a magnetic field, through which the extensions to more general Poincar\'e classes of spinor interactions are straightforwardly depicted.