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Near-field photon entanglement in total angular momentum

Nature volume 640, pages 634–640 (2025)Cite this article

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Abstract

Photons can carry angular momentum, which is conventionally attributed to two constituents—spin angular momentum (SAM), which is an intrinsic property related to the polarization, and orbital angular momentum (OAM), which is related to the photon spatial distribution. In paraxial optics, these two forms of angular momentum are separable1, such that entanglement can be induced between the SAM and the OAM of a single photon2,3 or of different photons in a multi-photon state4. In nanophotonic systems, however, the SAM and the OAM of a photon are inseparable5,6, so only the total angular momentum (TAM) serves as a good quantum number7,8,9. Here we present the observation of non-classical correlations between two photons in the near-field regime, giving rise to entanglement related to the TAM. We entangle those nanophotonic states by coupling photon pairs to plasmonic modes and use quantum imaging techniques10,11 to measure their correlations. We observe that entanglement in TAM leads to a completely different structure of quantum correlations of photon pairs, compared with entanglement related to the two constituent angular momenta. This work paves the way for on-chip quantum information processing using the TAM of photons as the encoding property for quantum information.

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Fig. 1: Nanophotonics vector field components.
Fig. 2: Heralded measurements of a single near-field photon.
Fig. 3: Non-classical correlations between nanophotonic states.
Fig. 4: Non-classical correlations measured in Fourier space.

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Data availability

The experimental data that support the findings presented in the paper and Supplementary Information and are available at https://github.com/yigali/near-field-ent-tam.

Code availability

The codes that support the findings presented here are available from https://github.com/yigali/near-field-ent-tam.

Change history

  • 01 May 2025

    In the version of this article initially published, there was an error in the order of color keys in Fig. 3j, where |ψ2⟩ appeared with the bottom blue bar and |ψ1⟩ appeared with the top red bar; the key has been amended in the HTML and PDF versions of the article.

References

  1. Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C. & Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992).

    Article  ADS  CAS  PubMed  Google Scholar 

  2. Stav, T. et al. Quantum entanglement of the spin and orbital angular momentum of photons using metamaterials. Science 361, 1101–1104 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  3. Karimi, E. et al. Spin-orbit hybrid entanglement of photons and quantum contextuality. Phys. Rev. A 82, 022115 (2010).

  4. Pan, J.-W. et al. Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777–838 (2012).

    Article  ADS  Google Scholar 

  5. Gorodetski, Y., Niv, A., Kleiner, V. & Hasman, E. Observation of the spin-based plasmonic effect in nanoscale structures. Phys. Rev. Lett. 101, 043903 (2008).

    Article  ADS  CAS  PubMed  Google Scholar 

  6. Bliokh, K. Y., Rodríguez-Fortuño, F. J., Nori, F. & Zayats, A. V. Spin–orbit interactions of light. Nat. Photon. 9, 796–808 (2015).

    Article  ADS  CAS  Google Scholar 

  7. Li, C.-F. Spin and orbital angular momentum of a class of nonparaxial light beams having a globally defined polarization. Phys. Rev. A 80, 063814 (2009).

    Article  ADS  Google Scholar 

  8. Zhao, Y., Edgar, J. S., Jeffries, G. D. M., McGloin, D. & Chiu, D. T. Spin-to-orbital angular momentum conversion in a strongly focused optical beam. Phys. Rev. Lett. 99, 073901 (2007).

    Article  ADS  PubMed  Google Scholar 

  9. Krenn, M., Tischler, N. & Zeilinger, A. On small beams with large topological charge. New J. Phys. 18, 033012 (2016).

    Article  ADS  Google Scholar 

  10. Defienne, H., Reichert, M. & Fleischer, J. W. General model of photon-pair detection with an image sensor. Phys. Rev. Lett. 120, 203604 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  11. Ndagano, B. et al. Imaging and certifying high-dimensional entanglement with a single-photon avalanche diode camera. npj Quantum Inf. 6, 94 (2020).

    Article  ADS  Google Scholar 

  12. Wang, J., Sciarrino, F., Laing, A. & Thompson, M. G. Integrated photonic quantum technologies. Nat. Photon. 14, 273–284 (2020).

    Article  ADS  CAS  Google Scholar 

  13. Madsen, L. S. et al. Quantum computational advantage with a programmable photonic processor. Nature 606, 75–81 (2022).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  14. Faraon, A. et al. Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade. Nat. Phys. 4, 859–863 (2008).

    Article  ADS  CAS  Google Scholar 

  15. O’Brien, J. L., Furusawa, A. & Vučković, J. Photonic quantum technologies. Nat. Photon. 3, 687–695 (2009).

    Article  ADS  Google Scholar 

  16. Reddy, D. V., Nerem, R. R., Nam, S. W., Mirin, R. P. & Verma, V. B. Superconducting nanowire single-photon detectors with 98% system detection efficiency at 1550 nm. Optica 7, 1649 (2020).

    Article  ADS  Google Scholar 

  17. Harrow, A. W. & Montanaro, A. Quantum computational supremacy. Nature 549, 203–209 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  18. Krenn, M., Hochrainer, A., Lahiri, M. & Zeilinger, A. Entanglement by path identity. Phys. Rev. Lett. 118, 080401 (2017).

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  19. Halder, M. et al. Entangling independent photons by time measurement. Nat. Phys. 3, 692–695 (2007).

    Article  CAS  Google Scholar 

  20. Reimer, C. et al. Generation of multiphoton entangled quantum states by means of integrated frequency combs. Science 351, 1176–1180 (2016).

    Article  ADS  CAS  PubMed  Google Scholar 

  21. Mair, A., Vaziri, A., Weihs, G. & Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001).

    Article  ADS  CAS  PubMed  Google Scholar 

  22. Nagali, E. et al. Quantum information transfer from spin to orbital angular momentum of photons. Phys. Rev. Lett. 103, 013601 (2009).

    Article  ADS  PubMed  Google Scholar 

  23. Molina-Terriza, G., Torres, J. P. & Torner, L. Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum. Phys. Rev. Lett. 88, 013601 (2001).

    Article  ADS  PubMed  Google Scholar 

  24. Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).

    Article  ADS  CAS  PubMed  Google Scholar 

  25. Simon, C. & Pan, J.-W. Polarization entanglement purification using spatial entanglement. Phys. Rev. Lett. 89, 257901 (2002).

    Article  ADS  PubMed  Google Scholar 

  26. Müller, M., Bounouar, S., Jöns, K. D., Glässl, M. & Michler, P. On-demand generation of indistinguishable polarization-entangled photon pairs. Nat. Photon. 8, 224–228 (2014).

    Google Scholar 

  27. Fabre, C. & Treps, N. Modes and states in quantum optics. Rev. Mod. Phys. 92, 035005 (2020).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  28. Devlin, R. C., Ambrosio, A., Rubin, N. A., Mueller, J. P. B. & Capasso, F. Arbitrary spin-to–orbital angular momentum conversion of light. Science 358, 896–901 (2017).

    Article  ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  29. Beth, R. A. Mechanical detection and measurement of the angular momentum of light. Phys. Rev. 50, 115–125 (1936).

    Article  ADS  Google Scholar 

  30. Fickler, R. et al. Quantum entanglement of high angular momenta. Science 338, 640–643 (2012).

    Article  ADS  CAS  PubMed  Google Scholar 

  31. Wang, J. et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photon. 6, 488–496 (2012).

    Article  ADS  CAS  Google Scholar 

  32. Fickler, R. et al. Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information. Nat. Commun. 5, 4502 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  33. Ostrovsky, E., Cohen, K., Tsesses, S., Gjonaj, B. & Bartal, G. Nanoscale control over optical singularities. Optica 5, 283 (2018).

    Article  ADS  CAS  MATH  Google Scholar 

  34. Tsesses, S., Cohen, K., Ostrovsky, E., Gjonaj, B. & Bartal, G. Spin–orbit interaction of light in plasmonic lattices. Nano Lett. 19, 4010–4016 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  35. Van Enk, S. J. & Nienhuis, G. Commutation rules and eigenvalues of spin and orbital angular momentum of radiation fields. J. Mod. Opt. 41, 963–977 (1994).

    Article  ADS  Google Scholar 

  36. Das, P., Yang, L.-P. & Jacob, Z. What are the quantum commutation relations for the total angular momentum of light? tutorial. J. Opt. Soc. Am. B 41, 1764 (2024).

    Article  CAS  Google Scholar 

  37. Shitrit, N. et al. Spin-optical metamaterial route to spin-controlled photonics. Science 340, 724–726 (2013).

    Article  ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  38. Kher-Aldeen, J. et al. Dynamic control and manipulation of near-fields using direct feedback. Light Sci. Appl. 13, 298 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  39. Lopez-Mago, D. & Gutiérrez-Vega, J. C. Shaping Bessel beams with a generalized differential operator approach. J. Opt. 18, 095603 (2016).

    Article  ADS  Google Scholar 

  40. Soares, W. C., Caetano, D. P. & Hickmann, J. M. Hermite–Bessel beams and the geometrical representation of nondiffracting beams with orbital angular momentum. Opt. Express 14, 4577 (2006).

    Article  ADS  CAS  PubMed  Google Scholar 

  41. Frischwasser, K. et al. Real-time sub-wavelength imaging of surface waves with nonlinear near-field optical microscopy. Nat. Photon. 15, 442–448 (2021).

    Article  ADS  CAS  Google Scholar 

  42. Milione, G., Sztul, H. I., Nolan, D. A. & Alfano, R. R. Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light. Phys. Rev. Lett. 107, 053601 (2011).

    Article  ADS  PubMed  Google Scholar 

  43. Dieleman, F., Tame, M. S., Sonnefraud, Y., Kim, M. S. & Maier, S. A. Experimental verification of entanglement generated in a plasmonic system. Nano Lett. 17, 7455–7461 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  44. Tame, M. S. et al. Quantum plasmonics. Nat. Phys. 9, 329–340 (2013).

    Article  CAS  Google Scholar 

  45. Fakonas, J. S., Mitskovets, A. & Atwater, H. A. Path entanglement of surface plasmons. New J. Phys. 17, 023002 (2015).

    Article  ADS  Google Scholar 

  46. Dowling, J. P. Quantum optical metrology—the lowdown on high-N00N states. Contemp. Phys. 49, 125–143 (2008).

    Article  ADS  CAS  Google Scholar 

  47. Howell, J. C., Bennink, R. S., Bentley, S. J. & Boyd, R. W. Realization of the Einstein–Podolsky–Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion. Phys. Rev. Lett. 92, 210403 (2004).

    Article  ADS  PubMed  Google Scholar 

  48. Bavaresco, J. et al. Measurements in two bases are sufficient for certifying high-dimensional entanglement. Nat. Phys. 14, 1032–1037 (2018).

    Article  CAS  Google Scholar 

  49. Dai, D. Silicon nanophotonic integrated devices for on-chip multiplexing and switching. J. Lightwave Technol. 35, 572–587 (2017).

    Article  ADS  CAS  Google Scholar 

  50. Orcutt, J. S. et al. Nanophotonic integration in state-of-the-art CMOS foundries. Opt. Express 19, 2335 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  51. Olivieri, L. et al. Terahertz nonlinear ghost imaging via plane decomposition: toward near-field micro-volumetry. ACS Photon. 10, 1726–1734 (2023).

    Article  CAS  Google Scholar 

  52. Ryczkowski, P., Barbier, M., Friberg, A. T., Dudley, J. M. & Genty, G. Ghost imaging in the time domain. Nat. Photon. 10, 167–170 (2016).

    Article  ADS  CAS  Google Scholar 

  53. Popov, E. (ed.) Gratings: Theory and Numeric Applications, Second Revisited Edition (Institut Fresnel, 2014).

  54. Johnson, K. C. Projection operator method for biperiodic diffraction gratings with anisotropic/bianisotropic generalizations. J. Opt. Soc. Am. A 31, 1698 (2014).

    Article  ADS  Google Scholar 

  55. Hong, M., Dawkins, R. B., Bertoni, B., You, C. & Magaña-Loaiza, O. S. Nonclassical near-field dynamics of surface plasmons. Nat. Phys. 20, 830–835 (2024).

    Article  CAS  Google Scholar 

  56. Lawrie, B. J., Evans, P. G. & Pooser, R. C. Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons. Phys. Rev. Lett. 110, 156802 (2013).

    Article  ADS  CAS  PubMed  Google Scholar 

  57. Huck, A. et al. Demonstration of quadrature-squeezed surface plasmons in a gold waveguide. Phys. Rev. Lett. 102, 246802 (2009).

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  58. Fasel, S. et al. Energy-time entanglement preservation in plasmon-assisted light transmission. Phys. Rev. Lett. 94, 110501 (2005).

    Article  ADS  PubMed  Google Scholar 

  59. Altewischer, E., van Exter, M. P. & Woerdman, J. P. Plasmon-assisted transmission of entangled photons. Nature 418, 304–306 (2002).

    Article  ADS  CAS  PubMed  Google Scholar 

  60. Chang, D. E., Sørensen, A. S., Hemmer, P. R. & Lukin, M. D. Quantum optics with surface plasmons. Phys. Rev. Lett. 97, 053002 (2006).

    Article  ADS  CAS  PubMed  Google Scholar 

  61. Ren, X. F., Guo, G. P., Huang, Y. F., Li, C. F. & Guo, G. C. Plasmon-assisted transmission of high-dimensional orbital angular-momentum entangled state. Europhys. Lett. 76, 753–759 (2006).

    Article  ADS  CAS  Google Scholar 

  62. Machado, F., Rivera, N., Buljan, H., Soljačić, M. & Kaminer, I. Shaping polaritons to reshape selection rules. ACS Photon. 5, 3064–3072 (2018).

    Article  CAS  Google Scholar 

  63. Bliokh, K. Y., Niv, A., Kleiner, V. & Hasman, E. Geometrodynamics of spinning light. Nat. Photon. 2, 748–753 (2008).

    Article  ADS  CAS  Google Scholar 

  64. Spektor, G., David, A., Gjonaj, B., Bartal, G. & Orenstein, M. Metafocusing by a metaspiral plasmonic lens. Nano Lett. 15, 5739–5743 (2015).

    Article  ADS  CAS  PubMed  Google Scholar 

  65. Kam, A. et al. Non-classical correlation between mode-entangled pairs of surface plasmon polaritons. In Proc. CLEO: Fundamental Science FF2C.5 (Optica Publishing Group, 2023).

  66. Wright, W. E. Parallelization of Bresenham’s line and circle algorithms. IEEE Comput. Graph. Appl. 10, 60–67 (1990).

    Article  Google Scholar 

  67. Gareth, J., Daniela, W., Trevor, H. & Robert, T. An Introduction to Statistical Learning Vol. 112 (Springer, 2013).

  68. Ilin, Y. & Arad, I. Learning a quantum channel from its steady-state. New J. Phys. 26, 073003 (2024).

    Article  MathSciNet  Google Scholar 

  69. Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. Preprint at https://arxiv.org/abs/1412.6980 (2014).

  70. Pelucchi, E. et al. The potential and global outlook of integrated photonics for quantum technologies. Nat. Rev. Phys. 4, 194–208 (2021).

    Article  Google Scholar 

  71. Loredo, J. C. et al. Generation of non-classical light in a photon-number superposition. Nat. Photon. 13, 803–808 (2019).

    Article  ADS  CAS  Google Scholar 

  72. Crespi, A. et al. Integrated photonic quantum gates for polarization qubits. Nat. Commun. 2, 566 (2011).

    Article  ADS  PubMed  Google Scholar 

  73. Marsili, F. et al. Detecting single infrared photons with 93% system efficiency. Nat. Photon. 7, 210–214 (2013).

    Article  ADS  CAS  Google Scholar 

  74. Wang, J. et al. Multidimensional quantum entanglement with large-scale integrated optics. Science 360, 285–291 (2018).

    Article  ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  75. Sit, A. et al. High-dimensional intracity quantum cryptography with structured photons. Optica 4, 1006 (2017).

    Article  ADS  Google Scholar 

  76. Reid, M. D. et al. The Einstein–Podolsky–Rosen paradox: from concepts to applications. Rev. Mod. Phys. 81, 1727–1751 (2009).

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This research was supported by the Israeli innovation authority through the MAGNET programme, grant number 73756, and was supported by the Israel Science Foundation (ISF), grant number 3620/24. We acknowledge the Russell Berrie Nanotechnology Institute, Micro-Nano Fabrication Unit (MNFU) and the Hellen Diller Quantum Center for their support of this research. A.K. acknowledges support by the programme for graduate students in the fields of natural sciences, engineering and medical professions by Israel Ministry of Innovation, Science, and Technology and the support from Helen Diller Quantum Center at the Technion. S.T. acknowledges support from the Adams fellowship programme of the Israel Academy of Science and Humanities, the Rothschild fellowship of the Yad Hanadiv foundation, the VATAT-Quantum fellowship of the Israel Council for Higher Education, the Helen Diller Quantum Center postdoctoral fellowship, and the Viterbi fellowship of the Technion – Israel Institute of Technology.

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Author notes

  1. These authors contributed equally: Amit Kam, Shai Tsesses

Authors and Affiliations

  1. Physics Department, Technion – Israel Institute of Technology, Haifa, Israel

    Amit Kam, Yaakov Lumer, Anatoly Patsyk, Liat Nemirovsky-Levy & Mordechai Segev

  2. Andrew and Erna Viterbi department of Electrical and Computer Engineering, Technion – Israel Institute of Technology, Haifa, Israel

    Shai Tsesses, Yigal Ilin, Kobi Cohen, Lior Fridman, Stav Lotan, Meir Orenstein, Mordechai Segev & Guy Bartal

  3. Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Shai Tsesses

  4. Solid State Institute, Technion – Israel Institute of Technology, Haifa, Israel

    Yaakov Lumer, Anatoly Patsyk, Liat Nemirovsky-Levy & Mordechai Segev

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Contributions

G.B., S.T. and M.S. conceived of the project. A.K., S.T. and K.C. designed and fabricated the samples. A.K., S.T., Y.L., L.F. and A.P. built the experimental platform. A.K., L.F. and S.T. conducted the measurements. A.K., S.T., S.L. and Y.I. performed the simulations and analysed the experimental results. A.K., S.T., L.N.-L. and M.O. conducted the theoretical calculations. G.B., M.O., S.T. and M.S. supervised the project. All authors participated in writing the paper.

Corresponding author

Correspondence to Guy Bartal.

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Extended data figures and tables

Extended Data Fig. 1 Coupling coefficient of the couplers.

Coupling coefficient as a function of the slit width and the grating period. Red dots represent the chosen configuration for our experiments. a. spiral in-coupler b. circular out-coupler.

Extended Data Fig. 2 SAM photo of the sample and cross-section of the couplers.

a. SAM photo of the experimental platform. in yellow the spiral coupler cross-section and in purple the circular out-coupler cross-section. b. The spiral input coupler (left photo), which creates the SPP entanglement is milled through the entire gold layer. c. The circular out-coupler ring (right photo) is milled only through 80 nm from it, scattering only SPPs towards the camera.

Extended Data Fig. 3 Experimental measurement of non-classical correlation.

a. Average intensity image of the of the plasmons that were out-coupled from the inner ring, in the case where two photons with circular polarization (\(|{\psi }_{1}\rangle \)) were launched. b-c. Examples of two correlation images (logarithmic scale) for the green and blue pixels marked in a. Highly positive correlations between antipodal pixels of the out-coupler give evidence of non-classical correlation between SPP pairs, indicating linear (elongated) states. d-f. Correlations of the out-coupled photons for the case where the two photons are launched with linear polarization (\(|{\psi }_{2}\rangle \)). Highly positive correlation with many pixels distributed along the circular coupler indicating a circularly symmetric state.

Extended Data Fig. 4 Explanation of the notation in the algorithm description.

Top row: Single correlative pixel case. Given a source pixel denoted by P, first we find the pixel denoted by O located on the outer radius \({R}_{2}\) of the annulus, such that the line from pixel P to pixel O intersects with the center of the annulus (see main text). We then traverse in clockwise direction on the outer radius \({R}_{2}\). Once the correlative pixel marked by the red square is found at angle \(\theta \), we increase the counter for the bin the angle \(\theta \) belongs to by \(+1\). Bottom row: Multiple correlative pixels case. The steps are exactly the same as for the single correlative pixel case, only now the counter in each bin is always normalized by the total sum of all counters across all bins, such that the resulting histogram will represent a valid probability distribution with respect to angle bins.

Extended Data Fig. 5 Correlation widths using the standard deviation.

a. The conditional probability distribution of the relative outcoupled angle of the entangled photons. b. Projection of joint probability distribution along the pulse-coordinates \({k}_{1}+{k}_{2}\). c. The conditional probability distribution of the relative transverse momentum of the entangled photons. The widths of the distributions determine the uncertainties in inferring the position or the momentum of one photon from that of the other. The solid lines are the theoretical predictions, and the dots are the experimental data.

Supplementary information

Supplementary Information

Supplementary Sections 1 and 2, including Supplementary Figs. 1 and 2—see contents for details.

Supplementary Video 1

Demonstrating the experimental set-up.

Supplementary Video 2

Non-classical correlations video for the state \(|{\psi }_{1}\rangle \). The green star symbolizes the pixel for which correlations are computed, and the heatmap represents the accumulated positive correlation with all green-star pixels thus far, showing high non-classical correlations between pixels at opposite sides of the out-coupler.

Supplementary Video 3

Non-classical correlations video for the state \(|{\psi }_{2}\rangle \). The green star symbolizes the pixel for which correlations are computed, and the heatmap represents the accumulated positive correlation with all green-star pixels thus far, showing high non-classical correlation with many, uniformly distributed, pixels in the out-coupler.

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Kam, A., Tsesses, S., Ilin, Y. et al. Near-field photon entanglement in total angular momentum. Nature 640, 634–640 (2025). https://doi.org/10.1038/s41586-025-08761-1

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