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arXiv:2405.11799 · Physical review. D/Physical review. D.

Regularized entanglement entropy of electron-positron scattering with a witness photon

Shanmuka Shivashankara, Grace Gogliettino

Published Nov 4, 2024• 5 citations
arXivHTMLPDF

Abstract

Regularized quantum information metrics are calculated for the scattering process e − e + → γ , Z → μ − μ + that has a witness photon entangled with the initial electron-positron state. Unitarity implies the correct regularization of divergences that appear in both the final density matrix and von Neumann entanglement entropies. The entropies are found to quantify uncertainty or randomness. The variation of information, entanglement entropy, and correlation between the muon’s and witness photon’s helicities are found to convey equivalent information. The magnitude of the muon’s expected helicity rises (falls) as the helicity entropy falls (rises). Area, or the scattering cross section, is a source of entropy for the muon’s helicity entropy and momentum entropy. The muon’s differential angular entropy distribution is similar to the differential angular cross section distribution, capturing the forward-backward asymmetry at high center-of-mass energies. Published by the American Physical Society 2024

DOI
10.1103/physrevd.110.096004

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Regularized quantum information metrics are calculated for the scattering process e − e + → γ , Z → μ − μ + that has a witness photon entangled with the initial electron-positron state. Unitarity implies the correct regularization of divergences that appear in both the final density matrix and von Neumann entanglement entropies. The entropies are found to quantify uncertainty or randomness. The variation of information, entanglement entropy, and correlation between the muon’s and witness photon’s helicities are found to convey equivalent information. The magnitude of the muon’s expected helicity rises (falls) as the helicity entropy falls (rises). Area, or the scattering cross section, is a source of entropy for the muon’s helicity entropy and momentum entropy. The muon’s differential angular entropy distribution is similar to the differential angular cross section distribution, capturing the forward-backward asymmetry at high center-of-mass energies. Published by the American Physical Society 2024
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We study the behavior of entanglement between different degrees of freedom of scattering fermions, based on an exemplary QED scattering process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. The variation of entanglement entropy between two fermions from an initial state to the final state was computed, with respect to different entanglement between the ingoing particles. This variation of entanglement entropy is found to be proportional to an area quantity, the total cross section. We also study the spin-momentum and helicity-momentum entanglements within one particle in the aforementioned scattering process. The calculations of the relevant variations of mutual information in the same inertial frame reveals that, for a maximally entangled initial state, the scattering between the particles does not affect the degree of both of these entanglements of one particle in the final state. It is also found that the increasing degree of entanglement between two ingoing particles would restrict the generation of entanglement between spin (helicity) and momentum of one outgoing particle. And the entanglement between spin and momentum within one particle in the final state is shown to always be stronger than that for helicity-momentum for a general initial entanglement state, implying significantly distinct properties of entanglement for the helicity and spin perceived by an inertial observer.
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When two initially entangled photons each undergo Compton scattering, the scattered electrons become correlated. However, the final reduced density matrix of one scattered pair is not influenced by the other scattered pair due to unitarity. Herein, we keep unitarity up to tree level for Compton double scattering and obtain different results than recent literature. The initial four particles, where the initial photons are entangled, are written as a superposition of two states with a relative phase. The final density matrix has two area divergences that are regularized with unitarity. The regularization procedure, i.e. solving for the roots of a polynomial that represents the probability for no scattering, suggests a novel definition of the scattering cross-section. Vieta's formulas relate these divergences to finite cross-sections. For an initial pure state, the formulas for the final density matrix and the correlation of final electronic polarizations are given. The correlation implies double scattering is analogous to Young's diffraction experiment. The two initial superposed states are the circular apertures while the Feynman amplitudes are the interfering complex light fields.
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