- Physical Review Journals
All JournalsPhysics Magazine

Physical Review A

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Entanglement, steering, and separability in Compton-scattered annihilation photons

Peter Caradonna1,* and Kenji Shimazoe1,2

  • *Contact author: petercaradonna65@gmail.com
PDF

Phys. Rev. A 112, 032413 – Published 5 September, 2025

DOI: https://doi.org/10.1103/j7p7-ckp9

Abstract

This work analyzes quantum correlations of photon pairs initially prepared in a Bell state, where one photon undergoes Compton scattering from a stationary, unpolarized electron. The evolved two-photon density matrix is analytically derived and spectrally decomposed. Concurrence and the Clauser-Horne-Shimony-Holt (CHSH) inequality evaluations identify angular regions demonstrating quantum steering correlations, entanglement without steering, and complete separability. The Peres conjecture is applied to interpret regions of entanglement lacking steering, emphasizing their limited practicality for quantum-information tasks. These results provide details potentially useful for employing Compton-scattered annihilation photons in various quantum protocols.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (37)

  1. N. Prantzos, C. Boehm, A. M. Bykov, R. Diehl, K. Ferrière, N. Guessoum, P. Jean, J. Knoedlseder, A. Marcowith, I. V. Moskalenko, A. Strong, and G. Weidenspointner, The 511 keV emission from positron annihilation in the galaxy, Rev. Mod. Phys. 83, 1001 (2011).
  2. A. Berera, Quantum coherence to interstellar distances, Phys. Rev. D 102, 063005 (2020).
  3. A. Berera and J. Calderón-Figueroa, Viability of quantum communication across interstellar distances, Phys. Rev. D 105, 123033 (2022).
  4. X.-M. Hu, Y. Guo, B.-H. Liu, C.-F. Li, and G.-C. Guo, Progress in quantum teleportation, Nat. Rev. Phys. 5, 339 (2023).
  5. I. Gauthier and M. Hawton, Photon correlations in positron annihilation, Phys. Rev. A 81, 062121 (2010).
  6. G. J. Rozing, P. E. Mijnarends, and R. Benedek, Fully relativistic calculation of the two-photon momentum distribution for positron annihilation in tungsten, Phys. Rev. B 43, 6996 (1991).
  7. S. D. Bass, S. Mariazzi, P. Moskal, and E. Stȩpień, Colloquium: Positronium physics and biomedical applications, Rev. Mod. Phys. 95, 021002 (2023).
  8. S. Basu, T. C. Kwee, S. Surti, E. A. Akin, D. Yoo, and A. Alavi, Fundamentals of PET and PET/CT imaging, Ann. N.Y. Acad. Sci. 1228, 1 (2011).
  9. E. Nevo, P. Kamvosoulis, and G. Currie, PET/MRI, part 3: Protocols and procedures, J. Nucl. Med. Technol. 50, 17 (2022).
  10. P. Caradonna, Kinematic analysis of multiple Compton scattering in quantum-entangled two-photon systems, Ann. Phys. (NY) 470, 169779 (2024).
  11. A. Zatcepin and S. I. Ziegler, Detectors in positron emission tomography, Z. Med. Phys. 33, 4 (2023), Special Issue: Recent Developments in Nuclear Medicine Imaging and Therapy.
  12. C. S. Levin, New imaging technologies to enhance the molecular sensitivity of positron emission tomography, Proc. IEEE 96, 439 (2008).
  13. H. Zaidi, M. L. Montandon, and S. Meikle, Strategies for attenuation compensation in neurological PET studies, NeuroImage 34, 518 (2007).
  14. D. Bohm and Y. Aharonov, Discussion of experimental proof for the paradox of Einstein, Rosen, and Podolsky, Phys. Rev. 108, 1070 (1957).
  15. P. Caradonna, I. D'Amico, D. G. Jenkins, and D. P. Watts, Stokes-parameter representation for Compton scattering of entangled and classically correlated two-photon systems, Phys. Rev. A 109, 033719 (2024).
  16. P. Caradonna, Compton scattering mediated by quantum entanglement, Phys. Rev. A 111, 053708 (2025).
  17. I. Tkachev, S. Musin, D. Abdurashitov, A. Baranov, F. Guber, A. Ivashkin, and A. Strizhak, Measuring the evolution of entanglement in Compton scattering, Sci. Rep. 15, 6064 (2025).
  18. J. Bordes, J. R. Brown, D. P. Watts, M. Bashkanov, K. Gibson, R. Newton, and N. Zachariou, First detailed study of the quantum decoherence of entangled gamma photons, Phys. Rev. Lett. 133, 132502 (2024).
  19. W. H. McMaster, Matrix representation of polarization, Rev. Mod. Phys. 33, 8 (1961).
  20. S. Shivashankara, Entanglement entropy of Compton scattering with a witness, Can. J. Phys. 101, 757 (2023).
  21. A. L. McNamara, M. Toghyani, J. E. Gillam, K. Wu, and Z. Kuncic, Towards optimal imaging with PET: An in silico feasibility study, Phys. Med. Biol. 59, 7587 (2014).
  22. H. Eslami and M. Mohamadian, Optimization of the positron emission tomography image resolution by using quantum entanglement concept, Eur. Phys. J. Plus 139, 976 (2024).
  23. D. Kim, A. N. Rachman, U. Taisei, M. Uenomachi, K. Shimazoe, and H. Takahashi, Background reduction in PET by double Compton scattering of quantum entangled annihilation photons, J. Instrum. 18, P07007 (2023).
  24. P. Moskal, Towards total-body modular PET for positronium and quantum entanglement imaging, in 2018 IEEE Nuclear Science Symposium and Medical Imaging Conference Proceedings (NSS/MIC) (IEEE, New York, 2018), pp. 1–4.
  25. A. M. Kožuljević, T. Bokulić, D. Grošev, Z. Kuncic, S. Parashari, L. Pavelić, and M. Makek, Investigation of the spatial resolution of PET imaging system measuring polarization-correlated Compton events, Nucl. Instrum. Methods Phys. Res. Sect. A 1068, 169795 (2024).
  26. S. Watanabe, S.-n. Ishikawa, H. Aono, S. Takeda, H. Odaka, M. Kokubun, T. Takahashi, K. Nakazawa, H. Tajima, M. Onishi, and Y. Kuroda, High energy resolution hard x-ray and gamma-ray imagers using CdTe diode devices, IEEE Trans. Nucl. Sci. 56, 777 (2009).
  27. M. Frandes, A. Zoglauer, V. Maxim, and R. Prost, A tracking Compton-scattering imaging system for hadron therapy monitoring, IEEE Trans. Nucl. Sci. 57, 144 (2010).
  28. M. Uenomachi, M. Takahashi, K. Shimazoe, H. Takahashi, K. Kamada, T. Orita, K. Ogane, and A. B. Tsuji, Simultaneous in vivo imaging with PET and SPECT tracers using a Compton-PET hybrid camera, Sci. Rep. 11, 17933 (2021).
  29. A. Wightman, Note on polarization effects in Compton scattering, Phys. Rev. 74, 1813 (1948).
  30. A. F. Abouraddy, A. V. Sergienko, B. E. Saleh, and M. C. Teich, Quantum entanglement and the two-photon stokes parameters, Opt. Commun. 201, 93 (2002).
  31. W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998).
  32. S. A. Hill and W. K. Wootters, Entanglement of a pair of quantum bits, Phys. Rev. Lett. 78, 5022 (1997).
  33. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880 (1969).
  34. R. Horodecki, P. Horodecki, and M. Horodecki, Violating Bell inequality by mixed spin-12 states: Necessary and sufficient condition, Phys. Lett. A 200, 340 (1995).
  35. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
  36. A. Peres, Collective tests for quantum nonlocality, Phys. Rev. A 54, 2685 (1996).
  37. A. Peres, Separability criterion for density matrices, Phys. Rev. Lett. 77, 1413 (1996).

Outline

Information

Phys. Rev. A 112, 032413– Published 5 September, 2025
  • Received 8 May 2025
  • Accepted 22 August 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation