Intrinsic quantum correlations for Gaussian localized Dirac cat states in phase space

TL;DR

This paper explores the phase-space representation of Gaussian localized Dirac cat states under a magnetic field, revealing persistent quantum correlations and intrinsic entanglement profiles through Wigner functions.

Contribution

It introduces a novel phase-space framework for Dirac cat states, analyzing their intrinsic entanglement and information dynamics using Wigner functions and Laguerre polynomials.

Findings

Dirac Wigner functions exhibit near-maximal persistent mutual information.

Quantum correlations depend on magnetic field intensity.

Phase-space analysis reveals interplay between classical and quantum spin-parity correlations.

Abstract

Following the information-based approach to Dirac spinors under a constant magnetic field, the phase-space representation of symmetric and anti-symmetric localized Dirac cat states is obtained. The intrinsic entanglement profile implied by the Dirac Hamiltonian is then investigated so as to shed a light on quantum states as carriers of qubits correlated by phase-space variables. Corresponding to the superposition of Gaussian states, cat states exhibit non-trivial elementary information dynamics which include the interplay between intrinsic entanglement and quantum superposition as reported by the corresponding Dirac archetypes. Despite the involved time-evolution as non-stationary states, the Wigner function constrains the elementary information quantifiers according to a robust framework which can be consistently used for quantifying the time-dependent $SU(2) \otimes SU(2)$ (spin projection and intrinsic parity) correlation profile of phase-space localized Dirac spinor states. Our results show that the Dirac Wigner functions for cat states -- described in terms of generalized Laguerre polynomials -- exhibit an almost maximized timely persistent mutual information profile which is engendered by either classical- or quantum-like spin-parity correlations, depending on the magnetic field intensity.