© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2511.22630 · Physics Letters B

A reconciliation of the Pryce-Ward and Klein-Nishina statistics for semi-classical simulations of annihilation photons correlations

Petar Žugec, Eric Andreas Vivoda, Mihael Makek, Ivica Friščić

quant-phphysics.data-anSubmitted Nov 27, 2025• Announced Nov 28, 2025• 1 citation• Revised Mar 13, 2026 (v2)

v1 · Nov 27, 2025 v2 · Mar 13, 2026

Abstract

Two photons from the ground state para-positronium annihilation are emitted in a maximally entangled singlet state of orthogonal polarizations. In case of the Compton scattering of both photons the phenomenon of quantum entanglement leads to a measurable increase in the azimuthal correlations of scattered photons, as opposed to a classical description treating the two scattering events as independent. The probability of the scattering of the system of the entangled photons is described by the Pryce-Ward cross section dependent on a difference of the azimuthal scattering angles in the fixed coordinate frame, while the independent scattering of single photons is described by the Klein-Nishina cross section dependent on the azimuthal angle relative to each photon's initial polarization. Since the singlet state of orthogonal polarizations is rotationally invariant, it does not carry any physical information on the initial polarizations of the single annihilation photons. In such bipartite state the angular origin for the Klein-Nishina cross section is undefined, making the Pryce-Ward and Klein-Nishina descriptions mutually exclusive. However, semi-classical simulations of the joint Compton scattering of entangled photons - implementing the Pryce-Ward cross section, but still treating the two photons as separate entities - can reconcile the Pryce-Ward correlations with the Klein-Nishina statistics for single photons by implementing a modified version of a scattering cross section presented in this work.

Journal reference: Physics Letters B 875 (2026) 140346
DOI: 10.1016/j.physletb.2026.140346
Comments: 15 pages, 3 figures

Related papers

Stokes-parameter representation for Compton scattering of entangled and classically correlated two-photon systems

Peter Caradonna, Irene D’Amico, D. G. Jenkins +1 more

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

Physical Review A•Mar 20, 2024•15 citations

Quantifying Quantum Correlations in Annihilation Photon Pairs under Compton Scattering

Z. AskariPour Ravari, Z. Riazi

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 $l_1$-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.

quant-pharXiv:2606.29035•The European Physical Journal Plus•Jun 30, 2026•0 citations

Closing the door on the “puzzle of decoherence” of annihilation quanta

Siddharth Parashari, D. Bosnar, Ivica Friščić +4 more

In positron annihilation, exploration of the polarization correlations of the emerging gamma quanta has gained interest, since they offer a possibility to improve signal-to-background in medical imaging using positron emission tomography. The annihilation quanta, which are predicted to be in an entangled state, have orthogonal polarizations and this property may be exploited to discriminate them from two uncorrelated gamma photons contributing to the background. Recent experimental studies of polarization correlations of the annihilation quanta after a prior Compton scattering of one of them, had rather different conclusions regarding the strength of the correlation after the scattering, showing its puzzling nature. The scattering was described as a decoherence process. In the present work, we perform for the first time, a study of the polarization correlations of annihilation quanta after decoherence via Compton scattering in the angular range 0∘−50∘ using single-layer gamma ray polarimeters. In addition, we compare the measured polarization correlations after Compton scattering at 30∘ with an active and a passive scatterer element. The measured azimuthal correlation of back-to-back annihilation quanta is consistent with the Pryce-Ward formulation, as confirmed by Monte Carlo simulations. Further, the results indicate that the correlation, expressed in terms of the polarimetric modulation factor, shows no significant difference at small scattering angles (0∘−30∘) compared to the correlation measured for direct photons, while a moderate indication of a lower modulation is observed for 50∘ scattering angle. The measured modulation is larger at all scattering angles than the one expected from the simulation of orthogonally polarized, independent annihilation quanta.

arXiv:2304.11362•Physics Letters B•Apr 5, 2024•15 citations

Entangled photons from para-positronium decay: Do coincidences from scattered photons imply a Bell state?

Paul Joos, Peter Kling

Electron and positron can form a meta-stable bound state called positronium that decays via pair annihilation. We show how polarization-dependent Compton scattering can be used to verify that the two annihilation photons in the spin-zero case (para-positronium) are emitted in a maximally entangled Bell state. Our theoretical approach based on two-photon density matrices connects concepts from relativistic quantum electrodynamics and quantum information theory.

quant-pharXiv:2606.31726•Jul 1, 2026•0 citations

Study of the Compton Scattering of Entangled Annihilation Photons

Alexander O. Strizhak, J. N. Abdurashitov, А. Г. Баранов +2 more

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.

Physics of Particles and Nuclei Letters•Oct 1, 2022•6 citations

Experimental observation of polarization correlation of entangled photons from positronium atom using J-PET detector

Deepak Kumar, Sushil Kumar Sharma, Paweł Moskal

Quantum entanglement is one of the fundamental correlations between particles that has not yet been confirmed with high-energy photons. Quantum electrodynamics (QED) predicts that annihilation photons produced by the decay of the singlet state of positronium (Ps) atoms are entangled in their polarization. Since these photons have an energy of 511 keV, there is no polarizer to measure the polarization of these photons. However, the direction of the scattering photons when interacting with an electron via the Compton process depends strongly on the polarization of the photon. Therefore, Compton scattering can be used as a polarization analyser. The polarization direction of the photon can be defined as the cross product of the momentum vector of the incident and scattered photon. By measuring the polarization of annihilation photons originating from Ps decays, their polarization correlation can be determined. Measuring this correlation will for the first time, will answer the open question of studying quantum entanglement in high-energy photons. Moreover, it also have potential applications in PET imaging, where the quality of image reconstruction directly depends on the selection of pure annihilation photons, which can be separated based on the strength of the polarization correlation. In this paper, we report on the method for determining the polarization correlation of annihilation photons using the J-PET detector.

European Physical Society Conference on High Energy Physics (EPS-HEP)•Dec 14, 2023•2 citations

Two photons from the ground state para-positronium annihilation are emitted in a maximally entangled singlet state of orthogonal polarizations. In case of the Compton scattering of both photons the phenomenon of quantum entanglement leads to a measurable increase in the azimuthal correlations of scattered photons, as opposed to a classical description treating the two scattering events as independent. The probability of the scattering of the system of the entangled photons is described by the Pryce-Ward cross section dependent on a difference of the azimuthal scattering angles in the fixed coordinate frame, while the independent scattering of single photons is described by the Klein-Nishina cross section dependent on the azimuthal angle relative to each photon's initial polarization. Since the singlet state of orthogonal polarizations is rotationally invariant, it does not carry any physical information on the initial polarizations of the single annihilation photons. In such bipartite state the angular origin for the Klein-Nishina cross section is undefined, making the Pryce-Ward and Klein-Nishina descriptions mutually exclusive. However, semi-classical simulations of the joint Compton scattering of entangled photons - implementing the Pryce-Ward cross section, but still treating the two photons as separate entities - can reconcile the Pryce-Ward correlations with the Klein-Nishina statistics for single photons by implementing a modified version of a scattering cross section presented in this work.

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

l_1

-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.

In positron annihilation, exploration of the polarization correlations of the emerging gamma quanta has gained interest, since they offer a possibility to improve signal-to-background in medical imaging using positron emission tomography. The annihilation quanta, which are predicted to be in an entangled state, have orthogonal polarizations and this property may be exploited to discriminate them from two uncorrelated gamma photons contributing to the background. Recent experimental studies of polarization correlations of the annihilation quanta after a prior Compton scattering of one of them, had rather different conclusions regarding the strength of the correlation after the scattering, showing its puzzling nature. The scattering was described as a decoherence process. In the present work, we perform for the first time, a study of the polarization correlations of annihilation quanta after decoherence via Compton scattering in the angular range 0∘−50∘ using single-layer gamma ray polarimeters. In addition, we compare the measured polarization correlations after Compton scattering at 30∘ with an active and a passive scatterer element. The measured azimuthal correlation of back-to-back annihilation quanta is consistent with the Pryce-Ward formulation, as confirmed by Monte Carlo simulations. Further, the results indicate that the correlation, expressed in terms of the polarimetric modulation factor, shows no significant difference at small scattering angles (0∘−30∘) compared to the correlation measured for direct photons, while a moderate indication of a lower modulation is observed for 50∘ scattering angle. The measured modulation is larger at all scattering angles than the one expected from the simulation of orthogonally polarized, independent annihilation quanta.

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.

Quantum entanglement is one of the fundamental correlations between particles that has not yet been confirmed with high-energy photons. Quantum electrodynamics (QED) predicts that annihilation photons produced by the decay of the singlet state of positronium (Ps) atoms are entangled in their polarization. Since these photons have an energy of 511 keV, there is no polarizer to measure the polarization of these photons. However, the direction of the scattering photons when interacting with an electron via the Compton process depends strongly on the polarization of the photon. Therefore, Compton scattering can be used as a polarization analyser. The polarization direction of the photon can be defined as the cross product of the momentum vector of the incident and scattered photon. By measuring the polarization of annihilation photons originating from Ps decays, their polarization correlation can be determined. Measuring this correlation will for the first time, will answer the open question of studying quantum entanglement in high-energy photons. Moreover, it also have potential applications in PET imaging, where the quality of image reconstruction directly depends on the selection of pure annihilation photons, which can be separated based on the strength of the polarization correlation. In this paper, we report on the method for determining the polarization correlation of annihilation photons using the J-PET detector.