Nonlocal transfer of high-dimensional unitary operations

Dilip Paneru; Francesco Di Colandrea; Alessio D'Errico; Ebrahim Karimi

doi:10.22331/q-2025-09-11-1855

Nonlocal transfer of high-dimensional unitary operations

Dilip Paneru¹, Francesco Di Colandrea^1,2, Alessio D'Errico^1,3, and Ebrahim Karimi^1,3,4

¹Nexus for Quantum Technologies, University of Ottawa, K1N 5N6, Ottawa, ON, Canada
²Dipartimento di Fisica, Università degli Studi di Napoli Federico II, Complesso Universitario di Monte Sant'Angelo, Via Cintia, 80126 Napoli, Italy
³National Research Council of Canada, 100 Sussex Drive, Ottawa ON Canada, K1A 0R6
⁴Institute for Quantum Studies, Chapman University, Orange, California 92866, USA

Published:	2025-09-11, volume 9, page 1855
Editor:	Carlo Beenakker
Eprint:	arXiv:2412.09768v2
Doi:	https://doi.org/10.22331/q-2025-09-11-1855
Citation:	Quantum 9, 1855 (2025).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

Highly correlated biphoton states are powerful resources in quantum optics, both for fundamental tests of the theory and practical applications. In particular, high-dimensional spatial correlation has been used in several quantum information processing and sensing tasks, for instance, in ghost imaging experiments along with several quantum key distribution protocols. Here, we introduce a technique that exploits spatial correlations, whereby one can nonlocally access the result of an arbitrary unitary operator on an arbitrary input state without the need to perform any operation themselves. The method is experimentally validated on a set of spatially periodic unitary operations in one-dimensional and two-dimensional spaces. Our findings pave the way for efficiently distributing quantum simulations and computations in future instances of quantum networks where users with limited resources can nonlocally access the results of complex unitary transformations via a centrally located quantum processor.

Featured image: Experimental setup for the nonlocal transfer of complex unitary operations. Two parties share entangled photon pairs generated via SPDC. The target operator is realized as a space-dependent phase modulation using a spatial light modulator acting on one photon. By projecting onto a specific state, the protocol enables users with limited resources to nonlocally access the result of a computation performed elsewhere.

Popular summary

Quantum simulation and quantum computation tasks are often formulated under the implicit assumption of unlimited computational resources, but in practice, this is never the case. Real quantum devices are typically expensive and very limited in the kinds of operations they can perform. A natural question arises: can users with greater computational capabilities help others by sharing not just raw resources, but the actual outcomes of complex quantum operations?

In our work, we demonstrate that this can be achieved by leveraging one of the central concepts in quantum mechanics: entanglement. By preparing and sharing pairs of strongly correlated photons, we show that it is possible for one party to nonlocally access the result of a quantum operation carried out elsewhere, without performing the operation themselves. The price to pay is the entanglement resource, which is sacrificed to transfer the outcome of the computation.

Our experimental realization validates this technique, dubbed "nonlocal transfer", for a family of spatial operations, both in one and two dimensions, implemented with a spatial light modulator in combination with a single-photon, time-stamping camera. This approach paves the way for efficiently distributing quantum simulations across different nodes of quantum networks, where the capability of quantum processors is not only shared but distributed in entirely new ways.

► BibTeX data

@article{Paneru2025nonlocaltransferof,
  doi = {10.22331/q-2025-09-11-1855},
  url = {https://doi.org/10.22331/q-2025-09-11-1855},
  title = {Nonlocal transfer of high-dimensional unitary operations},
  author = {Paneru, Dilip and Di Colandrea, Francesco and D'Errico, Alessio and Karimi, Ebrahim},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1855},
  month = sep,
  year = {2025}
}

► References

[1] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
https://doi.org/10.1103/RevModPhys.81.865

[2] D. Paneru, E. Cohen, R. Fickler, R. W. Boyd, and E. Karimi, Entanglement: quantum or classical?, Rep. Progr. Phys. 83, 064001 (2020).
https://doi.org/10.1088/1361-6633/ab85b9

[3] A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 47, 777 (1935).
https://doi.org/10.1103/PhysRev.47.777

[4] J. S. Bell, On the einstein podolsky rosen paradox, Physics Physique Fizika 1, 195 (1964).
https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195

[5] R. Jozsa and N. Linden, On the role of entanglement in quantum-computational speed-up, Proc. R. Soc. Lond. A 459, 2011 (2003).
https://doi.org/10.1098/rspa.2002.1097

[6] V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photonics 5, 222 (2011).
https://doi.org/10.1038/nphoton.2011.35

[7] R. Demkowicz-Dobrzański and L. Maccone, Using entanglement against noise in quantum metrology, Phys. Rev. Lett. 113, 250801 (2014).
https://doi.org/10.1103/PhysRevLett.113.250801

[8] C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, Theor. Comput. Sci. 560, 7 (2014).
https://doi.org/10.1016/j.tcs.2014.05.025

[9] R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, et al., Entanglement-based quantum communication over 144 km, Nat. Phys. 3, 481 (2007).
https://doi.org/10.1038/nphys629

[10] C. K. Hong and L. Mandel, Theory of parametric frequency down conversion of light, Phys. Rev. A 31, 2409 (1985).
https://doi.org/10.1103/PhysRevA.31.2409

[11] S. P. Walborn, C. Monken, S. Pádua, and P. S. Ribeiro, Spatial correlations in parametric down-conversion, Phys. Rep. 495, 87 (2010).
https://doi.org/10.1016/j.physrep.2010.06.003

[12] A. Aspect, J. Dalibard, and G. Roger, Experimental test of bell's inequalities using time-varying analyzers, Phys. Rev. Lett. 49, 1804 (1982).
https://doi.org/10.1103/PhysRevLett.49.1804

[13] D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, Experimental quantum teleportation, Nature 390, 575 (1997a).
https://doi.org/10.1038/37539

[14] P.-A. Moreau, E. Toninelli, T. Gregory, and M. J. Padgett, Imaging with quantum states of light, Nat. Rev. Phys. 1, 367 (2019).
https://doi.org/10.1038/s42254-019-0056-0

[15] J. H. Shapiro and R. W. Boyd, The physics of ghost imaging, Quantum Inf. Process. 11, 949 (2012).
https://doi.org/10.1007/s11128-011-0356-5

[16] F. Devaux, A. Mosset, F. Bassignot, and E. Lantz, Quantum holography with biphotons of high schmidt number, Phys. Rev. A 99, 033854 (2019).
https://doi.org/10.1103/PhysRevA.99.033854

[17] D. Zia, N. Dehghan, A. D’Errico, F. Sciarrino, and E. Karimi, Interferometric imaging of amplitude and phase of spatial biphoton states, Nat. Photonics 17, 1009 (2023).
https://doi.org/10.1038/s41566-023-01272-3

[18] E. Schrödinger, Discussion of probability relations between separated systems, Mathematical Proceedings of the Cambridge Philosophical Society 31, 555–563 (1935).
https://doi.org/10.1017/S0305004100013554

[19] E. Schrödinger, Probability relations between separated systems, Mathematical Proceedings of the Cambridge Philosophical Society 32, 446–452 (1936).
https://doi.org/10.1017/S0305004100019137

[20] H. M. Wiseman, S. J. Jones, and A. C. Doherty, Steering, entanglement, nonlocality, and the einstein-podolsky-rosen paradox, Phys. Rev. Lett. 98, 140402 (2007).
https://doi.org/10.1103/PhysRevLett.98.140402

[21] S. F. Huelga, M. B. Plenio, G.-Y. Xiang, J. Li, and G.-C. Guo, Remote implementation of quantum operations, J. Opt. B: Quantum Semiclass. Opt. 7, S384 (2005).
https://doi.org/10.1088/1464-4266/7/10/026

[22] H. Bechmann-Pasquinucci and W. Tittel, Quantum cryptography using larger alphabets, Phys. Rev. A 61, 062308 (2000).
https://doi.org/10.1103/PhysRevA.61.062308

[23] S. Designolle, V. Srivastav, R. Uola, N. H. Valencia, W. McCutcheon, M. Malik, and N. Brunner, Genuine high-dimensional quantum steering, Phys. Rev. Lett. 126, 200404 (2021).
https://doi.org/10.1103/PhysRevLett.126.200404

[24] N. Herrera Valencia, V. Srivastav, M. Pivoluska, M. Huber, N. Friis, W. McCutcheon, and M. Malik, High-Dimensional Pixel Entanglement: Efficient Generation and Certification, Quantum 4, 376 (2020).
https://doi.org/10.22331/q-2020-12-24-376

[25] D. Gottesman and I. L. Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations, Nature 402, 390 (1999).
https://doi.org/10.1038/46503

[26] D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, Experimental quantum teleportation, Nature 390, 575 (1997b).
https://doi.org/10.1038/37539

[27] L. Caha, X. Coiteux-Roy, and R. Koenig, Single-qubit gate teleportation provides a quantum advantage, Quantum 8, 1548 (2024).
https://doi.org/10.22331/q-2024-12-04-1548

[28] W.-Q. Liu and H.-R. Wei, Quantum gate teleportation with the superposition of causal order, Phys. Rev. Appl. 23, 014064 (2025).
https://doi.org/10.1103/PhysRevApplied.23.014064

[29] Y.-F. Huang, X.-F. Ren, Y.-S. Zhang, L.-M. Duan, and G.-C. Guo, Experimental teleportation of a quantum controlled-not gate, Phys. Rev. Lett. 93, 240501 (2004).
https://doi.org/10.1103/PhysRevLett.93.240501

[30] W.-B. Gao, A. M. Goebel, C.-Y. Lu, H.-N. Dai, C. Wagenknecht, Q. Zhang, B. Zhao, C.-Z. Peng, Z.-B. Chen, Y.-A. Chen, and J.-W. Pan, Teleportation-based realization of an optical quantum two-qubit entangling gate, Proc. Natl. Acad. Sci. 107, 20869 (2010).
https://doi.org/10.1073/pnas.1005720107

[31] K. S. Chou, J. Z. Blumoff, C. S. Wang, P. C. Reinhold, C. J. Axline, Y. Y. Gao, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, Deterministic teleportation of a quantum gate between two logical qubits, Nature 561, 368 (2018).
https://doi.org/10.1038/s41586-018-0470-y

[32] Y. Wan, D. Kienzler, S. D. Erickson, K. H. Mayer, T. R. Tan, J. J. Wu, H. M. Vasconcelos, S. Glancy, E. Knill, D. J. Wineland, A. C. Wilson, and D. Leibfried, Quantum gate teleportation between separated qubits in a trapped-ion processor, Science 364, 875 (2019).
https://doi.org/10.1126/science.aaw9415

[33] N. de Silva, Efficient quantum gate teleportation in higher dimensions, Proc. R. Soc. A: Math. Phys. Eng. Sci. 477, 20200865 (2021).
https://doi.org/10.1098/rspa.2020.0865

[34] S. Goel, S. Leedumrongwatthanakun, N. H. Valencia, W. McCutcheon, A. Tavakoli, C. Conti, P. W. Pinkse, and M. Malik, Inverse design of high-dimensional quantum optical circuits in a complex medium, Nat. Phys. 20, 232 (2024).
https://doi.org/10.1038/s41567-023-02319-6

[35] A. D'Errico, F. Cardano, M. Maffei, A. Dauphin, R. Barboza, C. Esposito, B. Piccirillo, M. Lewenstein, P. Massignan, and L. Marrucci, Two-dimensional topological quantum walks in the momentum space of structured light, Optica 7, 108 (2020).
https://doi.org/10.1364/OPTICA.365028

[36] F. Di Colandrea, A. Babazadeh, A. Dauphin, P. Massignan, L. Marrucci, and F. Cardano, Ultra-long quantum walks via spin–orbit photonics, Optica 10, 324 (2023).
https://doi.org/10.1364/OPTICA.474542

[37] J. F. Fitzsimons, Private quantum computation: an introduction to blind quantum computing and related protocols, Npj Quantum Inf. 3, 23 (2017).
https://doi.org/10.1038/s41534-017-0025-3

[38] S.-H. Wei, B. Jing, X.-Y. Zhang, J.-Y. Liao, C.-Z. Yuan, B.-Y. Fan, C. Lyu, D.-L. Zhou, Y. Wang, G.-W. Deng, et al., Towards real-world quantum networks: A review, Laser Photonics Rev. 16, 2100219 (2022).
https://doi.org/10.1002/lpor.202100219

[39] A. Nomerotski, Imaging and time stamping of photons with nanosecond resolution in timepix based optical cameras, Nucl. Instrum. Methods Phys. Res. A 937, 26 (2019).
https://doi.org/10.1016/j.nima.2019.05.034

[40] A. Nomerotski, M. Chekhlov, D. Dolzhenko, R. Glazenborg, B. Farella, M. Keach, R. Mahon, D. Orlov, and P. Svihra, Intensified tpx3cam, a fast data-driven optical camera with nanosecond timing resolution for single photon detection in quantum applications, J. Instrum. 18 (01), C01023.
https://doi.org/10.1088/1748-0221/18/01/C01023

[41] E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram, Opt. Lett. 38, 3546 (2013).
https://doi.org/10.1364/OL.38.003546

[42] R. Gerhberg and W. Saxton, A practical algorithm for the determination of phase from image and diffraction plane picture, Optik 35, 237 (1972).

[43] J. R. Fienup, Phase retrieval algorithms: a comparison, Appl. Opt. 21, 2758 (1982).
https://doi.org/10.1364/AO.21.002758

[44] A. K. Ekert, Quantum cryptography based on bell's theorem, Phys. Rev. Lett. 67, 661 (1991).
https://doi.org/10.1103/PhysRevLett.67.661

[45] M. K. Joshi, C. Kokail, R. van Bijnen, F. Kranzl, T. V. Zache, R. Blatt, C. F. Roos, and P. Zoller, Exploring large-scale entanglement in quantum simulation, Nature 624, 539 (2023).
https://doi.org/10.1038/s41586-023-06768-0

[46] P. Hickson, Atmospheric and adaptive optics, Astron. Astrophys. Rev. 22, 76 (2014).
https://doi.org/10.1007/s00159-014-0076-9

[47] L. Scarfe, F. Hufnagel, M. F. Ferrer-Garcia, A. D’Errico, K. Heshami, and E. Karimi, Fast adaptive optics for high-dimensional quantum communications in turbulent channels, Commun. Phys. 8, 79 (2025).
https://doi.org/10.1038/s42005-025-01986-6

[48] P. Cho, P. M. Pellegrino, J. Bickford, and A. Bontzos, Investigation of turbulence-tolerant free-space optical communications via multiplane light conversion, Opt. Eng. 61, 116104 (2022).
https://doi.org/10.1117/1.OE.61.11.116104

[49] T. Jaouni, L. Scarfe, F. Bouchard, M. Krenn, K. Heshami, F. Di Colandrea, and E. Karimi, Predicting atmospheric turbulence for secure quantum communications in free space, Opt. Express 33, 10759 (2025).
https://doi.org/10.1364/OE.546606

[50] X. Shen, J. M. Kahn, and M. A. Horowitz, Compensation for multimode fiber dispersion by adaptive optics, Opt. Lett. 30, 2985 (2005).
https://doi.org/10.1364/OL.30.002985

[51] N. H. Valencia, S. Goel, W. McCutcheon, H. Defienne, and M. Malik, Unscrambling entanglement through a complex medium, Nat. Phys. 16, 1112 (2020).
https://doi.org/10.1038/s41567-020-0970-1

[52] A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Entanglement of the orbital angular momentum states of photons, Nature 412, 313 (2001).
https://doi.org/10.1038/35085529

[53] R. C. Devlin, A. Ambrosio, D. Wintz, S. L. Oscurato, A. Y. Zhu, M. Khorasaninejad, J. Oh, P. Maddalena, and F. Capasso, Spin-to-orbital angular momentum conversion in dielectric metasurfaces, Opt. Express 25, 377 (2017).
https://doi.org/10.1364/OE.25.000377

[54] C. Wang, Z. Fu, W. Mao, J. Qie, A. D. Stone, and L. Yang, Non-hermitian optics and photonics: from classical to quantum, Adv. Opt. Photon. 15, 442 (2023).
https://doi.org/10.1364/AOP.475477

[55] H.-S. Zhong, H. Wang, Y.-H. Deng, M.-C. Chen, L.-C. Peng, Y.-H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu, et al., Quantum computational advantage using photons, Science 370, 1460 (2020).
https://doi.org/10.1126/science.abe8770

[56] J. M. Arrazola, V. Bergholm, K. Brádler, T. R. Bromley, M. J. Collins, I. Dhand, A. Fumagalli, T. Gerrits, A. Goussev, L. G. Helt, et al., Quantum circuits with many photons on a programmable nanophotonic chip, Nature 591, 54 (2021).
https://doi.org/10.1038/s41586-021-03202-1

Cited by

[1] Maria Gorizia Ammendola, Nazanin Dehghan, Lukas Scarfe, Alessio D’Errico, Francesco Di Colandrea, Ebrahim Karimi, and Filippo Cardano, "Compact and programmable large-scale optical processor in free space", Light: Science & Applications 15 1, 179 (2026).

[2] Yi Zheng, Yuanbo Gong, Jinshi Xu, Chuanfeng Li, and Guangcan Guo, " The spatial state of biphotons: physics and applications in quantum imaging", Advanced Imaging 3 4, B00003 (2026).

[3] Aaqib Ali, Giovanni Scala, and Cosmo Lupo, "Optimal and robust error filtration for quantum information processing", Physical Review A 112 4, 042418 (2025).

[4] Ebrahim Karimi, Frontiers in Optics + Laser Science 2025 (FiO, LS) FTh3E.2 (2025) ISBN:978-1-957171-52-4.

[5] Alessio D'Errico, Nazanin Dehghan, Maria Gorizia Ammendola, Lukas Scarfe, Roohollah Ghobadi, Francesco Di Colandrea, Filippo Cardano, and Ebrahim Karimi, "Programmable photonic quantum walks on lattices with cyclic, toroidal, and cylindrical topology", arXiv:2506.19024, (2025).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-13 15:59:31) and SAO/NASA ADS (last updated successfully 2026-08-13 15:59:32). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.