Qedtool: Python Package Reconstructs Quantum Electrodynamics Correlations and Full States in Relativistic Frameworks

Quantum electrodynamics, the study of how light and matter interact, presents significant computational challenges when researchers attempt to fully characterise quantum states and correlations. To address this, Jesse Smeets from Eindhoven University of Technology, alongside Preslav Asenov and Alessio Serafini from University College London, developed QEDtool, a new Python package that performs complex numerical calculations in this field. The package allows scientists to specify initial quantum states and then reconstruct the full range of correlations that characterise the final state, even accounting for relativistic effects through built-in Lorentz transformations. This advancement provides a powerful new tool for exploring fundamental aspects of quantum physics and promises to accelerate research into quantum information and related areas.

This work introduces QEDtool, a Python package for performing numerical calculations in quantum electrodynamics, with a focus on reconstructing the internal states of particles, their correlations, and quantifying entanglement. The package calculates interactions by evaluating polarized Feynman amplitudes within a relativistic framework, allowing users to define both pure and mixed initial states of polarization. From these initial states and calculated amplitudes, QEDtool reconstructs correlations that fully characterize the polarization and entanglement within the system.

QEDtool Reconstructs Particle Polarization and Correlations

The research team developed QEDtool, a Python package designed for precise numerical calculations in quantum electrodynamics, with a focus on reconstructing the internal states of particles and their correlations. The package calculates interactions by evaluating polarized Feynman amplitudes within a relativistic framework, allowing users to define both pure and mixed initial states of polarization. From these initial states and calculated amplitudes, QEDtool reconstructs correlations that fully characterize the polarization of the final state particles, and can express these quantities in any inertial frame using built-in Lorentz transformations. Experiments reveal that the differential cross section for the annihilation process, where an electron and positron create two photons, decreases with increasing collision momentum for all angles.

Around a collision momentum of 400 keV, the rate of decrease in the differential cross section appears to slow at angles of 0 and π, compared to angles near π/2. At lower collision energies, the concurrence, a measure of entanglement, remains close to 0. 9, but drops towards zero around 400 keV, before moderately restoring at higher energies. The team also measured the two-photon Stokes parameters, finding that the degree of double linear polarization decreases with increasing collision energy. Further analysis demonstrates that for all collision momenta tested, the emitted photon pairs are circularly polarized when scattered forward or backward.

The S11 and S33 Stokes parameters exhibit symmetry around an angle of π/2, while S21 does not. The team computed the differential probability of the two-photon state for unpolarized initial conditions, achieving results that differ from established theoretical calculations by only 10 -16 , attributable to floating-point errors. By fixing the collision energy at 200 keV, the researchers investigated solid angle correlations, revealing detailed distributions of the emitted photons. They then applied a Lorentz boost of 0. 6 along the collision axis, demonstrating that the package accurately transforms angles and correlations to a different reference frame. This boost was sufficient to flip the helicity of one of the initial fermions, resulting in transformed two-photon correlations that reflect the Lorentz covariance of the helicity basis. The resulting data, presented as distributions of the differential cross section, concurrence, two-photon degree of polarization, and Stokes parameters, confirms the package’s ability to accurately model particle interactions and their transformations under Lorentz boosts.

QEDtool Reconstructs Quantum States and Correlations

This work presents QEDtool, a new Python package designed for performing numerical calculations in quantum electrodynamics, with a particular focus on reconstructing quantum states and correlations. The package calculates polarized Feynman amplitudes within a relativistic framework, allowing users to define initial scattering states with specific polarization properties. From these inputs, QEDtool reconstructs correlations that fully characterize polarization in the final state, and can express these quantities in different inertial frames using built-in Lorentz transformations. The development of QEDtool addresses a need for precise angle and energy-resolved quantum state descriptions, particularly relevant to emerging technologies such as quantum lithography and positron emission tomography. By providing a robust framework for calculating entanglement and polarization correlations in high-energy scattering processes, the package supports detailed characterizations of scattered quantum states, advancing the theoretical understanding of these phenomena. The authors acknowledge that a fully comprehensive theoretical framework for entanglement in complex scattering scenarios, such as those involving multiple Compton scattering events, remains an area for further investigation, with future work potentially focusing on extending the package’s capabilities to address these more intricate processes and refine the modelling of entanglement in realistic experimental conditions.