QEDtool: A Python package for numerical quantum information in quantum electrodynamics

Abstract

This is the manual of the first version of QEDtool, an object-oriented Python package that performs numerical quantum electrodynamics calculations, with focus on full state reconstruction in the internal degrees of freedom, correlations and entanglement quantification. Our package rests on the evaluation of Feynman amplitudes in the momentum-helicity basis within a relativistic framework. Users can specify both pure and mixed initial scattering states in polarization space. From the specified initial state and Feynman amplitudes, QEDtool reconstructs correlations that fully characterize the quantum polarization and entanglement within the final state. These quantities can be expressed in any inertial frame by arbitrary, built-in Lorentz transformations.

Figures (9)

• Figure 1: The differential cross section (a), the concurrence (b) and the degree of two-photon polarization (c) of the emitted photon pair created in the annihilation process $\mathrm{e}^+\mathrm{e}^- \to 2\gamma$. The results are computed in the CM frame over an interval of polar angles $\theta\in[0,\pi]$ with $\phi = 0$. Each colored line represents the aforementioned quantities for different collision momenta $|\mathbf{p}|$, ranging from 100 keV to 300 keV.
• Figure 2: The differential cross section (a), concurrence (b) and two-photon degree of polarization (c) of the photon pair created in the annihilation process $\mathrm{e}^+\mathrm{e}^- \to 2\gamma$. These results are for $\phi = 0$ and an interval of polar angles $\theta\in[0,2\pi]$ and initial electron-positron CM momenta $|\mathbf{p}|\in[0.1,1]$ MeV.
• Figure 3: The $S_{11}$, $S_{33}$ and $S_{21}$ two-photon Stokes parameters [(a), (b) and (c) respectively] of the emitted photon pair formed in the annihilation process $\mathrm{e}^+\mathrm{e}^- \to 2\gamma$. The results are for $\phi = 0$, polar angles $\theta\in[0,2\pi]$ and for electron(positron) CM momenta $|\mathbf{p}|\in[0.1,1]$ MeV.
• Figure 4: A comparison between the QEDtool and the literary [see Eq. (\ref{['eq:PS_dW']})] results [(a) and (b) respectively] of the unpolarized differential scattering probability $\partial_\Pi\mathcal{P}$ of the electron-positron annihilation $\mathrm{e}^+\mathrm{e}^- \to 2\gamma$. Here, $|\Delta|$ denotes the absolute difference between the two results [plotted in (c)], which is on the order of $10^{-16}$.
• Figure 5: The differential cross section (a), the concurrence (b), the two-photon degree of polarization (c), and three Stokes parameters (d-f) for an interval of polar angles $\theta\in[0,\pi]$, azimuthal angles $\phi \in [0, 2\pi]$, and an initial electron-positron CM momenta $|\mathbf{p}| = 200$ keV. The white dotted circle denotes ${\theta = \pi/2}$.