- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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
  • Letter
  • Open Access

Routing entanglement through quantum networks

Karl Pelka*, Matteo Aquilina, and André Xuereb†

  • *Contact author: karl.a.pelka@um.edu.mt
  • †Contact author: andre.xuereb@um.edu.mt
PDF

Phys. Rev. Research 8, L022062 – Published 29 June, 2026

DOI: https://doi.org/10.1103/hsc8-pv2s

Abstract

Entanglement, one of the clearest manifestations of nonclassical physics, holds significant promise for technological applications such as more secure communications and faster computations. In this Letter, we explore the use of nonreciprocal transport in a network of continuous-variable systems to route entanglement in one direction through the network. We develop the theory and discuss a potential realization of controllable flow of entanglement in quantum systems; our method employs only Gaussian interactions and engineered dissipation to break the symmetry. We also explore the conditions under which thermal fluctuations limit the distance over which the entanglement propagates and observe a counterintuitive behavior between this distance, the strength of the entanglement source, and the strength of the hopping through the network.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (53)

  1. M. Mohseni, P. Read, H. Neven, S. Boixo, V. Denchev, R. Babbush, A. Fowler, V. Smelyanskiy, and J. Martinis, Commercialize quantum technologies in five years, Nature (London) 543, 171 (2017).
  2. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
  3. A. Acín, I. Cirac, and M. Lewenstein, Entanglement percolation in quantum networks, Nat. Phys. 3, 256 (2007).
  4. H. J. Kimble, The quantum internet, Nature (London) 453, 1023 (2008).
  5. F. Xu, X. Ma, Q. Zhang, H. K. Lo, and J. W. Pan, Secure quantum key distribution with realistic devices, Rev. Mod. Phys. 92, 025002 (2020).
  6. S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Shamsul Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, Advances in quantum cryptography, Adv. Opt. Photon. 12, 1012 (2020).
  7. E. Pelucchi, G. Fagas, I. Aharonovich, D. Englund, E. Figueroa, Q. Gong, H. Hannes, J. Liu, C. Y. Lu, N. Matsuda, J. W. Pan, F. Schreck, F. Sciarrino, C. Silberhorn, J. Wang, and K. D. Jöns, The potential and global outlook of integrated photonics for quantum technologies, Nat. Rev. Phys. 4, 194 (2022).
  8. J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Quantum state transfer and entanglement distribution among distant nodes in a quantum network, Phys. Rev. Lett. 78, 3221 (1997).
  9. J. Yin, Y. H. Li, S. K. Liao, M. Yang, Y. Cao, L. Zhang, J. G. Ren, W. Q. Cai, W. Y. Liu, S. L. Li, et al., Entanglement-based secure quantum cryptography over 1,120 kilometres, Nature (London) 582, 501 (2020).
  10. A. Metelmann and A. A. Clerk, Nonreciprocal photon transmission and amplification via reservoir engineering, Phys. Rev. X 5, 021025 (2015).
  11. J. Kim, M. C. Kuzyk, K. Han, H. Wang, and G. Bahl, Non-reciprocal Brillouin scattering induced transparency, Nat. Phys. 11, 275 (2015).
  12. C. H. Dong, Z. Shen, C. L. Zou, Y. L. Zhang, W. Fu, and G. C. Guo, Brillouin-scattering-induced transparency and non-reciprocal light storage, Nat. Commun. 6, 6193 (2015).
  13. K. M. Sliwa, M. Hatridge, A. Narla, S. Shankar, L. Frunzio, R. J. Schoelkopf, and M. H. Devoret, Reconfigurable Josephson circulator/directional amplifier, Phys. Rev. X 5, 041020 (2015).
  14. F. Lecocq, L. Ranzani, G. A. Peterson, K. Cicak, R. W. Simmonds, J. D. Teufel, and J. Aumentado, Nonreciprocal microwave signal processing with a field-programmable Josephson amplifier, Phys. Rev. Appl. 7, 024028 (2017).
  15. Z. Shen, Y. L. Zhang, Y. Chen, C. L. Zou, Y. F. Xiao, X. B. Zou, F. W. Sun, G. C. Guo, and C. H. Dong, Experimental realization of optomechanically induced non-reciprocity, Nat. Photon. 10, 657 (2016).
  16. N. R. Bernier, L. D. Tóth, A. Koottandavida, M. A. Ioannou, D. Malz, A. Nunnenkamp, A. K. Feofanov, and T. J. Kippenberg, Nonreciprocal reconfigurable microwave optomechanical circuit, Nat. Commun. 8, 604 (2017).
  17. S. Barzanjeh, M. Wulf, M. Peruzzo, M. Kalaee, P. B. Dieterle, O. Painter, and J. M. Fink, Mechanical on-chip microwave circulator, Nat. Commun. 8, 953 (2017).
  18. G. A. Peterson, F. Lecocq, K. Cicak, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Demonstration of efficient nonreciprocity in a microwave optomechanical circuit, Phys. Rev. X 7, 031001 (2017).
  19. L. Mercier de Lépinay, E. Damskägg, C. F. Ockeloen-Korppi, and M. A. Sillanpää, Realization of directional amplification in a microwave optomechanical device, Phys. Rev. Appl. 11, 034027 (2019).
  20. H. Xu, A. A. Clerk, and J. G. E. Harris, Nonreciprocal control and cooling of phonon modes in an optomechanical system, Nature (London) 568, 65 (2019).
  21. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  22. S. Barzanjeh, A. Xuereb, S. Gröblacher, M. Paternostro, C. A. Regal, and E. M. Weig, Optomechanics for quantum technologies, Nat. Phys. 18, 15 (2022).
  23. A. Xuereb, C. Genes, and A. Dantan, Strong coupling and long-range collective interactions in optomechanical arrays, Phys. Rev. Lett. 109, 223601 (2012).
  24. P. Piergentili, L. Catalani, M. Bawaj, S. Zippilli, N. Malossi, R. Natali, D. Vitali, and G. Di Giuseppe, Two-membrane cavity optomechanics, New J. Phys. 20, 083024 (2018).
  25. M. Schmidt, S. Kessler, V. Peano, O. Painter, and F. Marquardt, Optomechanical creation of magnetic fields for photons on a lattice, Optica 2, 635 (2015).
  26. V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, Topological phases of sound and light, Phys. Rev. X 5, 031011 (2015).
  27. J. P. Mathew, J. del Pino, and E. Verhagen, Synthetic gauge fields for phonon transport in a nano-optomechanical system, Nat. Nanotechnol. 15, 198 (2020).
  28. S. Walter, and F. Marquardt, Classical dynamical gauge fields in optomechanics, New J. Phys. 18, 113029 (2016).
  29. G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, Collective dynamics in optomechanical arrays, Phys. Rev. Lett. 107, 043603 (2011).
  30. R. Lauter, C. Brendel, Steven J. M. Habraken, and F. Marquardt, Pattern phase diagram for two-dimensional arrays of coupled limit-cycle oscillators, Phys. Rev. E 92, 012902 (2015).
  31. R. Lauter, A. Mitra, and F. Marquardt, From Kardar-Parisi-Zhang scaling to explosive desynchronization in arrays of limit-cycle oscillators, Phys. Rev. E 96, 012220 (2017).
  32. C. A. Holmes, C. P. Meaney, and G. J. Milburn, Synchronization of many nanomechanical resonators coupled via a common cavity field, Phys. Rev. E 85, 066203 (2012).
  33. N. Lörch, S. E. Nigg, A. Nunnenkamp, R. P. Tiwari, and C. Bruder, Quantum synchronization blockade: energy quantization hinders synchronization of identical oscillators, Phys. Rev. Lett. 118, 243602 (2017).
  34. E. Amitai, N. Lörch, A. Nunnenkamp, S. Walter, and C. Bruder, Synchronization of an optomechanical system to an external drive, Phys. Rev. A 95, 053858 (2017).
  35. M. Zhang, G.S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, and M. Lipson, Synchronization of micromechanical oscillators using light, Phys. Rev. Lett. 109, 233906 (2012).
  36. M. Zhang, S. Shah, J. Cardenas, and M. Lipson, Synchronization and phase noise reduction in micromechanical oscillator arrays coupled through light, Phys. Rev. Lett. 115, 163902 (2015).
  37. M. F. Colombano, G. Arregui, N. E. Capuj, A. Pitanti, J. Maire, A. Griol, B. Garrido, A. Martinez, C. M. Sotomayor-Torres, and D. Navarro-Urrios, Synchronization of optomechanical nanobeams by mechanical interaction, Phys. Rev. Lett. 123, 017402 (2019).
  38. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, Laser cooling of a nanomechanical oscillator into its quantum ground state, Nature (London) 478, 89 (2011).
  39. J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, Sideband cooling of micromechanical motion to the quantum ground state, Nature (London) 475, 359 (2011).
  40. C. F. Ockeloen-Korppi, E. Damskägg, J. M. Pirkkalainen, M. Asjad, A. A. Clerk, F. Massel, M. J. Wooley, and M. A. Sillanpää, Stabilized entanglement of massive mechanical oscillators, Nature (London) 556, 478 (2018).
  41. R. Riedinger, A. Wallucks, I. Marinković, C. Löschnauer, M. Aspelmeyer, S. Hong, and S. Gröblacher, Remote quantum entanglement between two micromechanical oscillators, Nature (London) 556, 473 (2018).
  42. S. Barzanjeh, M. Aquilina, and A. Xuereb, Manipulating the flow of thermal noise in quantum devices, Phys. Rev. Lett. 120, 060601 (2018).
  43. L. Orr, S. A. Khan, N. Buchholz, S. Kotler, and A. Metelmann, High-purity entanglement of hot propagating modes using nonreciprocity, PRX Quantum 4, 020344 (2023).
  44. C. Gardiner and P. Zoller, Cascaded quantum systems, in Quantum Noise, 2nd ed., edited by H. Haken (Springer, New York, 2000), Chap. 12, pp. 397–414.
  45. See Supplemental Material at http://link.aps.org/supplemental/10.1103/hsc8-pv2s for the determination of the dynamic and noise matrices for the model used, the analysis of stability and physicality of the dynamical equations, and a determination of the operational parameters of the system under consideration.
  46. T. Linowski, A. Teretenkov, and Ł. Rudnicki, Dissipative evolution of quantum Gaussian states, Phys. Rev. A 106, 052206 (2022).
  47. M. Behr, P. Benner, and J. Heiland, Solution formulas for differential Sylvester and Lyapunov equations, Calcolo 56, 51 (2019).
  48. A. Serafini, Quantum Continuous Variables, 1st ed. (Taylor & Francis, Boca Raton, FL, 2000).
  49. G. Adesso, A. Serafini, and F. Illuminati, Extremal entanglement and mixedness in continuous variable systems, Phys. Rev. A 70, 022318 (2004).
  50. G. Adesso and F. Illuminati, Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states, Phys. Rev. A 72, 032334 (2005).
  51. A. Serafini, F. Illuminati, and S. De Siena, Symplectic invariants, entropic measures and correlations of Gaussian states, J. Phys. B: At. Mol. Opt. Phys. 37, L21 (2004).
  52. I. Pietikäinen, O. Černotik, and R. Filip, Combining Floquet and Lyapunov techniques for time-dependent problems in optomechanics and electromechanics, New J. Phys. 22, 063019 (2020).
  53. S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola, Microwave quantum illumination, Phys. Rev. Lett. 114, 080503 (2015).

Outline

Information

Phys. Rev. Research 8, L022062– Published 29 June, 2026
  • Received 14 February 2024
  • Revised 13 November 2025
  • Accepted 20 April 2026
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