Eur. Phys. J. Plus (2020) 135: 320
https://doi.org/10.1140/epjp/s13360-020-00323-w

Regular Article

Lorentz invariant quantum concurrence for spin–parity states

¹ Departamento de Física, Universidade Federal de São Carlos, PO Box 676, 13565-905, São Carlos, SP, Brazil
² Max Planck Institute for the Science of Light, Staudtstraße 2, 91058, Erlangen, Germany
³ Dipartimento di Fisica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, Italy
⁴ INFN Sezione di Napoli, Gruppo collegato di Salerno, Napoli, Italy

^* e-mail: alexeb@ufscar.br

Received: 21 August 2019
Accepted: 9 March 2020
Published online: 19 March 2020

Abstract

The quantum concurrence of spin–parity states is shown to be invariant under 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 corresponding to just one of the inequivalent representations enclosed by the 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 Poincaré classes of spinor interactions are straightforwardly depicted.