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Physical Review A

Compton scattering mediated by quantum entanglement

Peter Caradonna

Published May 8, 2025• 9 citations
Publisher

Abstract

In this paper, the 16 Stokes parameters of a two-photon system are organized into a $4\ifmmode\times\else\texttimes\fi{}4$ Stokes matrix. This formalism is then applied to analyze the polarization properties of annihilation photons produced by electron-positron annihilation, with a particular focus on their evolution during Compton scattering interactions. The study demonstrates that when one of the subsystems undergoes Compton scattering, quantum entanglement preserves the polarization symmetry between the scattered and noninteraction photons, while in the absence of entanglement, this symmetry is lost. Moreover, the method simplifies the calculation of the joint differential cross section for multiple scattering scenarios and provides a means to characterize the polarization properties of the individual subsystems. These findings highlight the impact of quantum correlations on scattering behavior, and they offer a framework for further investigation into the polarization dynamics of entangled photon pairs.

DOI
10.1103/physreva.111.053708

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In this paper, the 16 Stokes parameters of a two-photon system are organized into a 4\ifmmode×\else\texttimes\fi44\ifmmode\times\else\texttimes\fi{}44\ifmmode×\else\texttimes\fi4 Stokes matrix. This formalism is then applied to analyze the polarization properties of annihilation photons produced by electron-positron annihilation, with a particular focus on their evolution during Compton scattering interactions. The study demonstrates that when one of the subsystems undergoes Compton scattering, quantum entanglement preserves the polarization symmetry between the scattered and noninteraction photons, while in the absence of entanglement, this symmetry is lost. Moreover, the method simplifies the calculation of the joint differential cross section for multiple scattering scenarios and provides a means to characterize the polarization properties of the individual subsystems. These findings highlight the impact of quantum correlations on scattering behavior, and they offer a framework for further investigation into the polarization dynamics of entangled photon pairs.
A Stokes parameter representation for two-photon systems is developed to calculate cross sections for both entangled and classically correlated mixed states scattering off unpolarized and polarized Compton electrons. The cross section of Compton scattering for pairs of maximally entangled annihilation photons, generated by the disintegration of para-positronium, is compared with classical analogs. An analysis of the symmetrical properties and basis independence of these systems is conducted to elucidate the observed differences. We propose a method to establish an upper bound for identifying correlations influenced by entanglement. Furthermore, we calculate the cross section for Compton scattering of annihilation photons from spin-polarized electrons. A qualitative analysis reveals a contradiction to the contemporary assumption that Compton scattering acts as an entanglement kill switch. These findings contribute to a broader understanding of photon systems and their behavior in various scattering scenarios. Although the primary focus of this article is on Compton scattering, the formalism can be adapted to other interactions, provided that the Mueller matrix representation of the interaction is available. Published by the American Physical Society 2024
We present a theoretical study of the evolution of polarization entanglement and quantum coherence in 511 keV photon pairs produced by para-positronium decay during successive Compton scattering events. We start with a maximally entangled Bell state and employ the generalized Stokes-Mueller formalism to derive the two-photon density matrix following single-, double-, and triple-Compton scattering, explicitly considering both polar and azimuthal scattering geometries. Using this framework, we quantify the degradation of quantum correlations through concurrence (as a measure of entanglement) and the l1l_1l1​-norm (as a measure of coherence). Our results demonstrate that entanglement is highly sensitive to the scattering geometry and disappears near right-angle scattering, while quantum coherence remains finite even in regimes where entanglement vanishes completely. These findings provide a unified description of polarization-dependent decoherence in annihilation photon pairs and clarify the distinct roles of entanglement and coherence in realistic two-photon interactions. These results are relevant for quantum-enhanced positron emission tomography and highlight the persistence of quantum resources in scattering-dominated media.
The Compton scattering of an entangled pair of photons is studied. Using the resulting reduced density matrix, we demonstrate how to derive the Kraus operators for the interaction from the underlying fundamental theory, quantum electrodynamics. The normalization of the final density matrix of the entangled photons after the interaction is crucial to obtaining the correct probabilities and correlations. The reduced density matrix of the photon, which does not participate in the interaction directly, remains unchanged. It indicates that quantum effects in quantum sensing using an entangled photon pair can be observed only through the correlations or superposition of the entire pair. We relate our results to the Stokes parameters for determining polarizations and investigating the entangled states of photons from electron-positron annihilation in astrophysical systems.
Abstract The experimental setup for study of Compton scattering of entangled and decoherent annihilation gammas is described. These gammas are born in two-photon positron-electron annihilation. Polarizations of annihilation gammas are mutually orthogonal, while the polarization of each photon is indefinite. If one of the photons of the pair interacts with matter, the pair becomes decoherent and photons acquire the determined polarization states. The kinematics of Compton scattering depends on the polarization states and can be different for entangled and decoherent pairs of annihilation photons. The angular correlations of scattered gammas for both, entangled and decoherent states are measured and compared. It is shown, that the kinematics of Compton scattering are similar for both cases.
Unitarity and the optical theorem are used to derive the reduced density matrices of Compton scattering in the presence of a witness particle. Two photons are initially entangled wherein one photon participates in Compton scattering, while the other is a witness, i.e., does not interact with the electron. Unitarity is shown to require that the entanglement entropy of the witness photon does not change after its entangled partner undergoes scattering. The final mutual information of the electron's and witness particle’s polarizations is shown to be nonzero for low-energy Compton scattering. This indicates that the two particles became correlated in spite of no direct interaction. Assuming an initial maximally entangled state, the change in entanglement entropy of the scattered photon’s polarization is calculated in terms of Stokes parameters. A common ratio of areas occurs in the final reduced density matrix elements, von Neumann entropies, Stokes parameter, and mutual information. This common ratio consists of the Thomson scattering cross-section and an accessible regularized scattering area.
The experimental setup to study the difference between Compton scattering of entangled and decoherent annihilation photons is discussed. The pairs of entangled gammas are born in electron-positron annihilation at rest. The polarization state of each photon in such a pair is not definite and represents the superposition of horizontal and vertical polarizations, while the relative polarizations of the photons are orthogonal. After interaction with the environment (for example, via the Compton scattering) the entangled pair of photons is broken and the pair becomes decoherent with determined polarizations of both gammas. Since the Compton scattering depends on the polarization of the initial photon, the scattering kinematics of entangled and decoherent photons might be quite different. At present, there is no experimental comparison of the Compton scattering kinematics for entangled and decoherent gammas.