# Entanglement of Dirac bi-spinor states driven by Poincaré classes of $\mbox{SU}(2) \otimes \mbox{SU}(2)$ coupling potentials

**Authors:** Victor A. S. V. Bittencourt, Alex E. Bernardini  
**arXiv:** [1511.07047](https://arxiv.org/abs/1511.07047)  
**Date:** 2015-11-22  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1511.07047v3/

## Key points

- Paper title: "Entanglement of Dirac bi-spinor states driven by Poincaré classes of $\mbox{SU}(2) \otimes \mbox{SU}(2)$ coupling potentials"
- Authors: Victor A. S. V. Bittencourt and Alex E. Bernardini
- Analysis of entanglement and quantum correlation properties within Dirac-like structures influenced by Poincaré classes of external field potentials
- Impact of (pseudo)scalar, (pseudo)vector, and tensor interactions on quantum correlations in $\mbox{SU}(2) \otimes \mbox{SU}(2)$ bi-spinor structures
- Calculation of quantum entanglement (concurrence) and quantum correlations (geometric discord) using a suitable ansatz to derive the Dirac Hamiltonian eigenspinor structure
- Exploration of the interplay between different types of interactions and their influence on quantum phenomena
- Framework for incorporating localization effects and mapping quantum correlation effects onto Dirac-like systems describing low-energy excitations in materials like graphene and trapped ions
- Potential applications in understanding fundamental aspects of quantum mechanics in diverse contexts

## Summary

In their paper titled "Entanglement of Dirac bi-spinor states driven by Poincaré classes of $\mbox{SU}(2) \otimes \mbox{SU}(2)$ coupling potentials," authors Victor A. S. V. Bittencourt and Alex E. Bernardini present a comprehensive analysis of entanglement and quantum correlation properties within Dirac-like structures influenced by various Poincaré classes of external field potentials. The study delves into the impact of (pseudo)scalar, (pseudo)vector, and tensor interactions on the generation and disruption of intrinsic quantum correlations in $\mbox{SU}(2) \otimes \mbox{SU}(2)$ bi-spinor structures, considering the effects of generic coupling constants. By employing a suitable ansatz to derive the Dirac Hamiltonian eigenspinor structure for time-independent solutions of the associated Liouville equation, the authors calculate both quantum entanglement, measured through concurrence, and quantum correlations, assessed via geometric discord. These calculations are performed for various combinations of well-defined Poincaré classes of Dirac potentials, shedding light on the intricate interplay between different types of interactions and their influence on quantum phenomena. Furthermore, beyond its formal structure, the research results establish a framework that can be expanded to incorporate localization effects and map quantum correlation effects onto Dirac-like systems that describe low-energy excitations in materials such as graphene and trapped ions. This expansion opens up new avenues for exploring the behavior of entangled states in complex physical systems and highlights potential applications in understanding fundamental aspects of quantum mechanics in diverse contexts.