CP symmetry and thermal effects on Dirac bi-spinor spin-parity local correlations

TL;DR

This paper investigates the quantum correlations in Dirac bi-spinors, analyzing how CP symmetry, magnetic fields, and thermal effects influence entanglement and discord, revealing invariance of entanglement but sensitivity of discord to CP transformations.

Contribution

It provides a detailed analysis of spin-parity quantum correlations in Dirac bi-spinors, including effects of magnetic fields and thermal states, and examines their behavior under CP symmetry.

Findings

Quantum entanglement remains invariant under CP transformations.

Geometric discord is highly sensitive to CP symmetry.

Thermal effects influence the quantum correlations in Dirac bi-spinor states.

Abstract

Intrinsic quantum correlations supported by the $SU(2)\otimes SU(2)$ structure of the Dirac equation used to describe particle/antiparticle states, optical ion traps and bilayer graphene are investigated and connected to the description of local properties of Dirac bi-spinors. For quantum states driven by Dirac-like Hamiltonians, quantum entanglement and geometric discord between spin and parity degrees of freedom - sometimes mapped into equivalent low energy internal degrees of freedom - are obtained. Such \textit{spin-parity} quantum correlations and the corresponding nonlocal intrinsic structures of bi-spinor fermionic states can be classified in order to relate quantum observables to the (non)local behavior of these correlations. It is shown that free particle mixed states do not violate the Clauser-Horne-Shymony-Holt inequality: the correlations in such mixed bi-spinors, although quantum, can be reproduced by a suitable local hidden variable model. Additionally, the effects due to a non-minimal coupling to a homogeneous magnetic field, and to the inclusion of thermal effects are evaluated, and quantum correlations of associated quantum mixtures and of the thermal states are all quantified.The above-mentioned correlation quantifiers are then used to measure the influence of CP transformations on \textit{spin-parity} quantum correlations, and our results show that quantum entanglement is invariant under CP transformations, although the geometric discord is highly sensitive to the CP symmetry.