Quantum Information & Computation
Volume 25, Issue 2
RESEARCH ARTICLE Open access

A Survey on Continuous Variable Quantum Key Distribution for Secure Data Transmission: Toward the Future of Secured Quantum-Networks

Mobin Motaharifar, Mahmood Hasani, Hassan Kaatuzian

Author affiliations
  • Mobin Motaharifar1
  • Mahmood Hasani1
  • Hassan Kaatuzian1
  1. Photonics Research Laboratory, Electrical Engineering Dept, Amirkabir University of Technology, Tehran, Iran ;

pp. 175-194 · 10.2478/qic-2025-0009

Abstract

Quantum key distribution (QKD) represents a cornerstone of secure communication in the quantum era. While discrete-variable QKD (DV-QKD) protocols were historically the first to demonstrate secure key exchange, continuous-variable QKD (CV-QKD) has emerged as a more practical alternative due to its seamless compatibility with current telecommunications infrastructure. CV-QKD relies on coherent and squeezed states of light, offering significant advantages for integration into modern optical networks. This review comprehensively explores the theoretical underpinnings, technological advancements, and practical challenges of CV-QKD. Special attention is given to the role of photonic integrated circuits (PICs) in enabling scalable and efficient implementation of CV-QKD systems. Furthermore, recent advances in machine learning have been leveraged to optimize CV-QKD performance, with data-driven techniques enhancing noise estimation, parameter optimization, and system security. Additionally, tensor networks provide efficient computational tools for analyzing complex quantum correlations, improving the efficiency and robustness of quantum key distribution protocols. These developments, combined with ongoing improvements in quantum photonic integration, pave the way for the practical deployment of large-scale, high-speed quantum-secure networks.
Open accessCC BY-NC-ND 4.0

Keywords

  • squeezed light
  • quantum key distribution
  • continuous variable quantum key distribution
  • teleportation
  • photonic integrated circuit

Suggested citation

Mobin Motaharifar, Mahmood Hasani, Hassan Kaatuzian (2025). A Survey on Continuous Variable Quantum Key Distribution for Secure Data Transmission: Toward the Future of Secured Quantum-Networks. Quantum Information & Computation, 25(2), 175-194. https://doi.org/10.2478/qic-2025-0009

References (132)

  1. D. Stucki et al. (2011). “Long-term performance of the SwissQuantum quantum key distribution network in a field environment”. New Journal of Physics, 13: 12, 123001.DOI: 10.1088/1367-2630/13/12/123001Google Scholar
  2. M. Sasaki et al. (2011). “Field test of quantum key distribution in the Tokyo QKD Network”. Optics Express, 19: 11, 10387–10409.DOI: 10.1364/OE.19.010387Google Scholar
  3. R. J. Hughes, J. E. Nordholt, K. P. McCabe, R. T. Newell, C. G. Peterson, and R. D. Somma (2013). “Network-centric quantum communications with application to critical infrastructure protection”. arXiv preprint arXiv:1305.0305.DOI: 10.1364/FIO.2013.FW2C.1Google Scholar
  4. H.-K. Lo, M. Curty, and K. Tamaki (2014). “Secure quantum key distribution”. Nature Photonics, 8: 8, 595–604.DOI: 10.1038/nphoton.2014.149Google Scholar
  5. A. Orieux and E. Diamanti (2016). “Recent advances on integrated quantum communications”. Journal of Optics, 18: 8, 083002.DOI: 10.1088/2040-8978/18/8/083002Google Scholar
  6. P. Sibson et al. (2017). “Chip-based quantum key distribution”. Nature Communications, 8: 1, 13984.DOI: 10.1038/ncomms13984Google Scholar
  7. S. Tanzilli, A. Martin, F. Kaiser, M. P. De Micheli, O. Alibart, and D. B. Ostrowsky (2012). “On the genesis and evolution of integrated quantum optics”. Laser & Photonics Reviews, 6: 1, 115–143.DOI: 10.1002/lpor.201100010Google Scholar
  8. P. Zhang et al. (2014). “Reference-frame-independent quantum-key-distribution server with a telecom tether for an on-chip client”. Physical Review Letters, 112: 13, 130501.DOI: 10.1103/PhysRevLett.112.130501Google Scholar
  9. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien (2008). “Silica-on-silicon waveguide quantum circuits”. Science, 320: 5876, 646–649DOI: 10.1126/science.1155441Google Scholar
  10. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao (1996). “Writing waveguides in glass with a femtosecond laser”. Optics Letters, 21: 21, 1729–1731.DOI: 10.1364/OL.21.001729Google Scholar
  11. J. G. Huang et al. (2017). “Torsional frequency mixing and sensing in optomechanical resonators”. Applied Physics Letters, 111: 11.DOI: 10.1063/1.4986811Google Scholar
  12. Y. Shi et al. (2018). “Nanometer-precision linear sorting with synchronized optofluidic dual barriers”. Science Advances, 4: 1, p. eaao0773.DOI: 10.1126/sciadv.aao0773Google Scholar
  13. Y. Z. Shi et al. (2018). “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct bindingefficiency measurement”. Nature Communications, 9: 1, 815.DOI: 10.1038/s41467-018-03156-5Google Scholar
  14. A. Boaron et al. (2018). “Secure quantum key distribution over 421 km of optical fiber”. Physical Review Letters, 121: 19, 190502.DOI: 10.1103/PhysRevLett.121.190502Google Scholar
  15. H.-L. Yin et al. (2016). “Measurement-device-independent quantum key distribution over a 404 km optical fiber”. Physical Review Letters, 117: 19, 190501.DOI: 10.1103/PhysRevLett.117.190501Google Scholar
  16. Y.-M. Li, X.-Y. Wang, Z.-L. Bai, W.-Y. Liu, S.-S. Yang, and K.-C. Peng (2017). “Continuous variable quantum key distribution”. Chinese Physics B, 26: 4, 040303.DOI: 10.1088/1674-1056/26/4/040303Google Scholar
  17. C. H. Bennett and G. Brassard (2014). “Quantum cryptography: Public key distribution and coin tossing”. Theoretical Computer Science, 560: 7–11.DOI: 10.1016/j.tcs.2014.05.025Google Scholar
  18. C. H. Bennett (1992). “Quantum cryptography using any two nonorthogonal states”. Physical Review Letters, 68: 21, 3121.DOI: 10.1103/PhysRevLett.68.3121Google Scholar
  19. A. K. Ekert (1991). “Quantum cryptography and Bell’s theorem”. Quantum Measurements in Optics, 413–418.DOI: 10.1007/978-1-4615-3386-3_34Google Scholar
  20. L. Ma et al. (2023). “Practical continuous-variable quantum key distribution with feasible optimization parameters”. Science China Information Sciences, 66: 8, 180507.DOI: 10.1007/s11432-022-3712-3Google Scholar
  21. S. Sarmiento et al. (2022). “Continuous-variable quantum key distribution over a 15 km multi-core fiber”. New Journal of Physics, 24: 6, 063011.DOI: 10.1088/1367-2630/ac753bGoogle Scholar
  22. Y. Zhang, Y. Bian, Z. Li, S. Yu, and H. Guo (2024). “Continuous-variable quantum key distribution system: Past, present, and future”. Applied Physics Reviews, 11: 1.DOI: 10.1063/5.0179566Google Scholar
  23. S. Pirandola (2021). “Composable security for continuous variable quantum key distribution: Trust levels and practical key rates in wired and wireless networks”. Physical Review Research, 3: 4, 043014.DOI: 10.1103/PhysRevResearch.3.043014Google Scholar
  24. N. Wang, S. Du, W. Liu, X. Wang, Y. Li, and K. Peng (2018). “Long-distance continuous-variable quantum key distribution with entangled states”. Physical Review Applied, 10: 6, 064028.DOI: 10.1103/PhysRevApplied.10.064028Google Scholar
  25. C. Weedbrook et al. (2012). “Gaussian quantum information”. Reviews of Modern Physics, 84: 2, 621–669.DOI: 10.1103/RevModPhys.84.621Google Scholar
  26. G. Adesso, S. Ragy, and A. R. Lee (2014). “Continuous variable quantum information: Gaussian states and beyond”. Open Systems & Information Dynamics, 21: 01n02, 1440001.DOI: 10.1142/S1230161214400010Google Scholar
  27. A. Ferraro, S. Olivares, and M. G. Paris (2005). “Gaussian states in continuous variable quantum information”. arXiv preprint quant-ph/0503237.Google Scholar
  28. I. W. Primaatmaja, W. Y. Kon, and C. Lim (2024). “Discrete-modulated continuous-variable quantum key distribution secure against general attacks”. arXiv preprint arXiv:2409.02630.Google Scholar
  29. N. Alshaer, T. Ismail, and H. Mahmoud (2024). “Enhancing Performance of Continuous-Variable Quantum Key Distribution (CV-QKD) and Gaussian Modulation of Coherent States (GMCS) in Free-Space Channels under Individual Attacks with Phase-Sensitive Amplifier (PSA) and Homodyne Detection (HD)”. Sensors, 24: 16, 5201.DOI: 10.3390/s24165201Google Scholar
  30. S. Bäuml, C. Pascual-García, V. Wright, O. Fawzi, and A. Acín (2024). “Security of discrete-modulated continuous-variable quantum key distribution”. Quantum, 8: 1418.DOI: 10.22331/q-2024-07-18-1418Google Scholar
  31. P. Papanastasiou, C. Ottaviani, and S. Pirandola (2021). “Security of continuous-variable quantum key distribution against canonical attacks”, in 2021 International Conference on Computer Communications and Networks (ICCCN): IEEE, 1–6.DOI: 10.1109/ICCCN52240.2021.9522349Google Scholar
  32. A. G. Mountogiannakis, P. Papanastasiou, B. Braverman, and S. Pirandola (2022). “Composably secure data processing for Gaussian-modulated continuous-variable quantum key distribution”. Physical Review Research, 4: 1, 013099.DOI: 10.1103/PhysRevResearch.4.013099Google Scholar
  33. L. d. S. Aguiar, L. F. Borelli, J. A. Roversi, and A. Vidiella-Barranco (2022). “Performance analysis of continuous-variable quantum key distribution using non-Gaussian states”. Quantum Information Processing, 21: 8, 304.DOI: 10.1007/s11128-022-03645-zGoogle Scholar
  34. N. Hosseinidehaj, A. M. Lance, T. Symul, N. Walk, and T. C. Ralph (2020). “Finite-size effects in continuous-variable quantum key distribution with Gaussian postselection”. Physical Review A, 101: 5, 052335.DOI: 10.1103/PhysRevA.101.052335Google Scholar
  35. N. K. Long, R. Malaney, and K. J. Grant (2022). “A survey of machine learning assisted continuous-variable quantum key distribution”. Information, 14: 10, 553.DOI: 10.3390/info14100553Google Scholar
  36. H.-M. Chin, N. Jain, D. Zibar, U. L. Andersen, and T. Gehring (2021). “Machine learning aided carrier recovery in continuous-variable quantum key distribution”. npj Quantum Information, 7: 1, 20.DOI: 10.1038/s41534-021-00361-xGoogle Scholar
  37. Q. Liao, J. Liu, A. Huang, L. Huang, Z. Fei, and X. Fu (2023). “High-rate discretely-modulated continuous-variable quantum key distribution using quantum machine learning”. arXiv preprint arXiv:2308.03283.Google Scholar
  38. W.-B. Liu, C.-L. Li, Z.-P. Liu, M.-G. Zhou, H.-L. Yin, and Z.-B. Chen (2022). “Theoretical development of discrete-modulated continuous-variable quantum key distribution”. (in English), Frontiers in Quantum Science and Technology, Mini Review, 1: 985276, doi: 10.3389/frqst.2022.985276.DOI: 10.3389/frqst.2022.985276Google Scholar
  39. Y. Yan et al. (2023). “Artificial key fingerprints for continuous-variable quantum key distribution”. Physical Review A, 108: 1, 012601, doi: 10.1103/PhysRevA.108.012601.DOI: 10.1103/PhysRevA.108.012601Google Scholar
  40. C. Ding, S. Wang, Y. Wang, Z. Wu, J. Sun, and Y. Mao (2023). “Machine-learning-based detection for quantum hacking attacks on continuous-variable quantum-key-distribution systems”. Physical Review A, 107: 6, 062422, doi: 10.1103/PhysRevA.107.062422.DOI: 10.1103/PhysRevA.107.062422Google Scholar
  41. D. F. Walls (1983). “Squeezed states of light”. Nature, 306: 5939, 141–146.DOI: 10.1038/306141a0Google Scholar
  42. H. Lin and Y. Shang (2024). “Deterministic search on complete bipartite graphs by continuous time quantum walk”. arXiv preprint arXiv:2404.01640.DOI: 10.2478/qic-2024-0001Google Scholar
  43. B. Zhang and Q. Zhuang (2021). “Entanglement formation in continuous-variable random quantum networks”. npj Quantum Information, 7: 1, 33.DOI: 10.1038/s41534-021-00370-wGoogle Scholar
  44. C. S. Hamilton, R. Kruse, L. Sansoni, S. Barkhofen, C. Silberhorn, and I. Jex (2017). “Gaussian boson sampling”. Physical Review Letters, 119: 17, 170501.DOI: 10.1103/PhysRevLett.119.170501Google Scholar
  45. H.-S. Zhong et al. (2020). “Quantum computational advantage using photons”. Science, 370: 6523, 1460–1463.DOI: 10.1126/science.abe8770Google Scholar
  46. H.-S. Zhong et al. (2021). “Phase-programmable gaussian boson sampling using stimulated squeezed light”. Physical Review Letters, 127: 18, 180502.DOI: 10.1103/PhysRevLett.127.180502Google Scholar
  47. A. Czerwinski (2024). “Quantum state tomography of photonic qubits with realistic coherent light sources”. Quantum Information & Computation, 24: 31–39.DOI: 10.2478/qic-2024-0002Google Scholar
  48. R. Schnabel (2017). “Squeezed states of light and their applications in laser interferometers”. Physics Reports, 684: 1–51.DOI: 10.1016/j.physrep.2017.04.001Google Scholar
  49. H. Vahlbruch et al. (2008). “Observation of squeezed light with 10–dB quantum-noise reduction”. Physical Review Letters, 100: 3, 033602.DOI: 10.1103/PhysRevLett.100.033602Google Scholar
  50. H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel (2016). “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency”. Physical Review Letters, 117: 11, 110801.DOI: 10.1103/PhysRevLett.117.110801Google Scholar
  51. S. Du and Z. Bai (2024). “State convertibility under genuinely incoherent operations”. Quantum Information & Computation, 24: 17–30.DOI: 10.2478/qic-2024-0007Google Scholar
  52. S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J. H. Shapiro, and S. Pirandola (2015). “Microwave quantum illumination”. Physical Review Letters, 114: 8, 080503.DOI: 10.1103/PhysRevLett.114.080503Google Scholar
  53. H. Wang et al. (2020). “Observation of intensity squeezing in resonance fluorescence from a solid-state device”. Physical Review Letters, 125: 15, 153601.DOI: 10.1103/PhysRevLett.125.153601Google Scholar
  54. M. Sabatini, T. Bertapelle, P. Villoresi, G. Vallone, and M. Avesani (2024), “Hybrid encoder for discrete and continuous variable QKD”. arXiv preprint arXiv:2408.17412.DOI: 10.1002/qute.202400522Google Scholar
  55. R. Loudon and P. L. Knight (1987). “Squeezed light”. Journal of Modern Optics, 34: 6–7, 709–759.DOI: 10.1080/09500348714550721Google Scholar
  56. A. I. Lvovsky (2015). “Squeezed light”. Photonics: Scientific Foundations, Technology and Applications, 1: 121–163.DOI: 10.1002/9781119009719.ch5Google Scholar
  57. B. E. Saleh and M. C. Teich (2019). Fundamentals of Photonics. John Wiley & Sons.Google Scholar
  58. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger (1997). “Experimental quantum teleportation”. Nature, 390: 6660, 575–579.DOI: 10.1038/37539Google Scholar
  59. M. B. Plenio and S. Virmani (2005). “An introduction to entanglement measures”. arXiv preprint quant-ph/0504163.DOI: 10.1002/9783527618637.ch10Google Scholar
  60. M. Motaharifar, H. Kaatuzian, and M. Hasani (2023). “Possible teleportation of quantum states using squeezed sources and photonic integrated circuits”, in 2023 5th Iranian International Conference on Microelectronics (IICM), IEEE, 227–232.DOI: 10.1109/IICM60532.2023.10443082Google Scholar
  61. L. Albano, D. Mundarain, and J. Stephany (2002). “On the squeezed number states and their phase space representations”. Journal of Optics B: Quantum and Semiclassical Optics, 4: 5, 352.DOI: 10.1088/1464-4266/4/5/319Google Scholar
  62. M. A. Nielsen and I. L. Chuang (2010). Quantum Computation and Quantum Information. Cambridge University Press.Google Scholar
  63. M. Motaharifar and H. Kaatuzian (2023). "Mach-Zehnder interferometer cell for realization of quantum computerDOI: 10.1109/ICEE59167.2023.10334740Google Scholar
  64. a feasibility study", in 2023 31st International Conference on Electrical Engineering (ICEE). IEEE, 762-767.Google Scholar
  65. D. Dai and J. E. Bowers (2011). “Novel ultra-short and ultra-broadband polarization beam splitter based on a bent directional coupler”. Optics Express, 19: 19, 18614–18620.DOI: 10.1364/OE.19.018614Google Scholar
  66. J. Wang, D. Liang, Y. Tang, D. Dai, and J. E. Bowers (2013). “Realization of an ultra-short silicon polarization beam splitter with an asymmetrical bent directional coupler”. Optics Letters, 38: 1, 4–6.DOI: 10.1364/OL.38.000004Google Scholar
  67. T. C. Ralph (1999). “Continuous variable quantum cryptography”. Physical Review A, 61: 1, 010303.DOI: 10.1103/PhysRevA.61.010303Google Scholar
  68. M. Hillery (2000). “Quantum cryptography with squeezed states”. Physical Review A, 61: 2, 022309.DOI: 10.1103/PhysRevA.61.022309Google Scholar
  69. M. D. Reid (2000). “Quantum cryptography with a predetermined key, using continuous-variable Einstein-Podolsky-Rosen correlations”. Physical Review A, 62: 6, 062308.DOI: 10.1103/PhysRevA.62.062308Google Scholar
  70. N. J. Cerf, M. Levy, and G. Van Assche (2001). “Quantum distribution of Gaussian keys using squeezed states”. Physical Review A, 63: 5, 052311.DOI: 10.1103/PhysRevA.63.052311Google Scholar
  71. D. Gottesman and J. Preskill (2003). Quantum Information with Continuous Variables. Springer Dordrecht.Google Scholar
  72. F. Grosshans and P. Grangier (2002). “Continuous variable quantum cryptography using coherent states”. Physical Review Letters, 88: 5, 057902.DOI: 10.1103/PhysRevLett.88.057902Google Scholar
  73. A. Leverrier and P. Grangier (2009). “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation”. Physical Review Letters, 102: 18, 180504.DOI: 10.1103/PhysRevLett.102.180504Google Scholar
  74. X. Su, W. Wang, Y. Wang, X. Jia, C. Xie, and K. Peng (2009). “Continuous variable quantum key distribution based on optical entangled states without signal modulation”. Europhysics Letters, 87: 2, 20005.DOI: 10.1209/0295-5075/87/20005Google Scholar
  75. A. Denys, P. Brown, and A. Leverrier (2021). “Explicit asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation”. Quantum, 5: 540.DOI: 10.22331/q-2021-09-13-540Google Scholar
  76. L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen (2012). “Continuous variable quantum key distribution with modulated entangled states”. Nature Communications, 3: 1, 1083.DOI: 10.1038/ncomms2097Google Scholar
  77. V. C. Usenko and R. Filip (2011). “Squeezed-state quantum key distribution upon imperfect reconciliation”. New Journal of Physics, 13: 11, 113007.DOI: 10.1088/1367-2630/13/11/113007Google Scholar
  78. C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam (2004). “Quantum cryptography without switching”. Physical Review Letters, 93: 17, 170504.DOI: 10.1103/PhysRevLett.93.170504Google Scholar
  79. A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam (2005). “No-switching quantum key distribution using broadband modulated coherent light”. Physical Review Letters, 95: 18, 80503.DOI: 10.1103/PhysRevLett.95.180503Google Scholar
  80. R. García-Patrón and N. J. Cerf (2009). “Continuous-variable quantum key distribution protocols over noisy channels”. Physical Review Letters, 102: 13, 130501.DOI: 10.1103/PhysRevLett.102.130501Google Scholar
  81. J. Lodewyck et al. (2007). “Quantum key distribution over 25 km with an all-fiber continuous-variable system”. Physical Review A—Atomic, Molecular, and Optical Physics, 76: 4, 042305.DOI: 10.1103/PhysRevA.76.042305Google Scholar
  82. F. Grosshans, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier (2003). “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables”. arXiv preprint quant-ph/0306141DOI: 10.26421/QIC3.s-6Google Scholar
  83. G. Roberts et al. (2018). “Patterning-effect mitigating intensity modulator for secure decoy-state quantum key distribution”. Optics Letters, 43: 20, 5110–5113.DOI: 10.1364/OL.43.005110Google Scholar
  84. H.-K. Lo, M. Curty, and B. Qi (2012). “Measurement-device-independent quantum key distribution”. Physical Review Letters, 108: 13, 130503, doi: 10.1103/PhysRevLett.108.130503.DOI: 10.1103/PhysRevLett.108.130503Google Scholar
  85. Y. Ding et al. (2017). “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits”. npj Quantum Information, 3: 1, 25.DOI: 10.1038/s41534-017-0026-2Google Scholar
  86. C. Ma et al. (2016). “Silicon photonic transmitter for polarization-encoded quantum key distribution”. Optica, 3: 11, 1274–1278.DOI: 10.1364/OPTICA.3.001274Google Scholar
  87. P. Sibson, J. E. Kennard, S. Stanisic, C. Erven, J. L. O’Brien, and M. G. Thompson (2017). “Integrated silicon photonics for high-speed quantum key distribution”. Optica, 4: 2, 172–177.DOI: 10.1364/OPTICA.4.000172Google Scholar
  88. F. Najafi et al. (2015). “On-chip detection of non-classical light by scalable integration of single-photon detectors”. Nature Communications, 6: 1, 5873.DOI: 10.1038/ncomms6873Google Scholar
  89. W. H. Pernice et al. (2012). “High-speed and high-efficiency travelling wave single-photon detectors embedded in nanophotonic circuits”. Nature Communications, 3: 1, 1325.DOI: 10.1038/ncomms2307Google Scholar
  90. M. Ziebell et al. (2015). “Towards on-chip continuous-variable quantum key distribution”, in The European Conference on Lasers and Electro-Optics. Optica Publishing Group.Google Scholar
  91. P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti (2013). “Experimental demonstration of long-distance continuous-variable quantum key distribution”. Nature Photonics, 7: 5, 378–381.DOI: 10.1038/nphoton.2013.63Google Scholar
  92. D. Huang, P. Huang, D. Lin, and G. Zeng (2016). “Long-distance continuous-variable quantum key distribution by controlling excess noise”. Scientific Reports, 6: 1, 19201.DOI: 10.1038/srep19201Google Scholar
  93. F. Raffaelli et al. (2018). “A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers”. Quantum Science and Technology, 3: 2, 025003.DOI: 10.1088/2058-9565/aaa38fGoogle Scholar
  94. M. Rudé et al. (2018). “Interferometric photodetection in silicon photonics for phase diffusion quantum entropy sources”. Optics Express, 26: 24, 31957–31964.DOI: 10.1364/OE.26.031957Google Scholar
  95. F. Raffaelli, P. Sibson, J. E. Kennard, D. H. Mahler, M. G. Thompson, and J. C. Matthews (2018). “Generation of random numbers by measuring phase fluctuations from a laser diode with a silicon-on-insulator chip”. Optics Express, 26: 16, 19730–19741.DOI: 10.1364/OE.26.019730Google Scholar
  96. C. Abellan et al. (2016). “Quantum entropy source on an InP photonic integrated circuit for random number generation”. Optica, 3: 9, 989–994.DOI: 10.1364/OPTICA.3.000989Google Scholar
  97. P. Kaur, A. Boes, G. Ren, T. G. Nguyen, G. Roelkens, and A. Mitchell, (2021). “Hybrid and heterogeneous photonic integration”. APL Photonics, 6, 6.DOI: 10.1063/5.0052700Google Scholar
  98. K. Jaksch et al. (2024). “Composable free-space continuous-variable quantum key distribution using discrete modulation”. arXiv preprint arXiv:2410.12915.Google Scholar
  99. Y. Xu et al. (2021). “Hybrid external-cavity lasers (ECL) using photonic wire bonds as coupling elements”. Scientific Reports, 11: 1, 16426.DOI: 10.1038/s41598-021-95981-wGoogle Scholar
  100. C. Koos et al. (2013). “Photonic wire bonding: An enabling technology for heterogeneous multi-chip integration”, in Integrated Photonics Research, Silicon and Nanophotonics. Optica Publishing Group.DOI: 10.1364/IPRSN.2013.IM4A.3Google Scholar
  101. M. Hasani, H. Kaatuzian, and M. Motaharifar, (2023). “Stochastic mass-spring model for the generation of squeezed state of light”, in Laser Science. Optica Publishing Group.DOI: 10.1364/FIO.2023.JM7A.7Google Scholar
  102. S. Zhao et al. (2024). “Broadband amplitude squeezing at room temperature in electrically driven quantum dot lasers”. Physical Review Research, 6: 3, L032021.DOI: 10.1103/PhysRevResearch.6.L032021Google Scholar
  103. M. Hasani and M. Motaharifar, (2024). “Experimental realization of spontaneous parametric down conversion”.DOI: 10.1364/opticaopen.28024766.v1Google Scholar
  104. M. Rabiei, H. Kaatuzian, M. Hasani, and A. Shircharandabi, (2024). “Analysis of squeezed light generation via SFWM in a Si3N4microring resonator”, in Frontiers in Optics. Optica Publishing Group.DOI: 10.1364/FIO.2024.JD4A.30Google Scholar
  105. A. Shircharandabi, H. Kaatuzian, M. Hasani, and M. Rabiei, (2024). “Investigation of squeezed-state generation using SFWM in a SiO2 microring resonator”, in Laser Science. Optica Publishing Group.DOI: 10.1364/FIO.2024.JD4A.58Google Scholar
  106. E. Engin et al. (2013). “Photon pair generation in a silicon micro-ring resonator with reverse bias enhancement”. Optics Express, 21: 23, 27826–27834.DOI: 10.1364/OE.21.027826Google Scholar
  107. J. M. Arrazola et al. (2021). “Quantum circuits with many photons on a programmable nanophotonic chip”. Nature, 591: 7848, 54–60.DOI: 10.1038/s41586-021-03202-1Google Scholar
  108. M. A. Broome et al. (2013). “Photonic boson sampling in a tunable circuit”. Science, 339: 6121, 794–798.DOI: 10.1126/science.1231440Google Scholar
  109. A. Molina and J. Watrous, (2019). “Revisiting the simulation of quantum Turing machines by quantum circuits”. Proceedings of the Royal Society A, 475: 2226, 20180767.DOI: 10.1098/rspa.2018.0767Google Scholar
  110. R. Nagai, T. Tomono, and Y. Minato, (2021). “Simulation of Continuous-Variable Quantum Systems with Tensor Network”. in 2021 IEEE International Conference on Quantum Computing and Engineering (QCE). IEEE, 437–438.DOI: 10.1109/QCE52317.2021.00067Google Scholar
  111. Q. Zhang, H. Lai, J. Pieprzyk, and L. Pan, (2022). “An improved quantum network communication model based on compressed tensor network states”. Quantum Information Processing, 21: 7, 253.DOI: 10.1007/s11128-022-03609-3Google Scholar
  112. Q. Zhang, H. Lai, and J. Pieprzyk, (2022). “Quantum-key-expansion protocol based on number-stateentanglement-preserving tensor network with compression”. Physical Review A, 105: 3, 032439.DOI: 10.1103/PhysRevA.105.032439Google Scholar
  113. A. Rubenok, J. A. Slater, P. Chan, I. Lucio-Martinez, and W. Tittel, (2013). “Real-world two-photon interference and proof-of-principle quantum key distribution immune to detector attacks”. Physical Review Letters, 111: 13, 130501, doi: 10.1103/PhysRevLett.111.130501.DOI: 10.1103/PhysRevLett.111.130501Google Scholar
  114. T. Li, Z. Gao, and Z. Li, (2020). “Measurement-device–independent quantum secure direct communication: Direct quantum communication with imperfect measurement device and untrusted operator”. Europhysics Letters, 131: 6, 60001.DOI: 10.1209/0295-5075/131/60001Google Scholar
  115. Y. Cao et al. (2020). “Long-distance free-space measurement-device-independent quantum key distribution”. Physical Review Letters, 125: 26, 260503.Google Scholar
  116. Y.-H. Li et al. (2023). “Free-space and fiber-integrated measurement-device-independent quantum key distribution under high background noise”. Physical Review Letters, 131: 10, 100802.DOI: 10.1103/PhysRevLett.131.100802Google Scholar
  117. L. Cao et al. (2020). “Chip-based measurement-device-independent quantum key distribution using integrated silicon photonic systems”. Physical Review Applied, 14: 1, 011001.DOI: 10.1103/PhysRevApplied.14.011001Google Scholar
  118. Q. Liao, Y. Wang, D. Huang, and Y. Guo, (2018). “Dual-phase-modulated plug-and-play measurement-device-independent continuous-variable quantum key distribution”. Optics Express, 26: 16, 19907–19920.DOI: 10.1364/OE.26.019907Google Scholar
  119. P. Wang, Y. Tian, and Y. Li, (2025). “Advances in continuous variable measurement-device-independent quantum key distribution”. arXiv preprint arXiv:2502.16448.DOI: 10.1007/s11432-024-4491-9Google Scholar
  120. Y.-C. Zhang, Z. Li, S. Yu, W. Gu, X. Peng, and H. Guo, (2014). “Continuous-variable measurementdevice-independent quantum key distribution using squeezed states”. Physical Review A,. 90: 5, 052325, doi: 10.1103/PhysRevA.90.052325.DOI: 10.1103/PhysRevA.90.052325Google Scholar
  121. L. Fan, Y. Bian, Y. Zhang, and S. Yu, (2022). “Free-space continuous-variable quantum key distribution with imperfect detector against uniform fast-fading channels”. Symmetry, 14: 6, 1271. https://www.mdpi.com/2073-8994/14/6/1271.DOI: 10.3390/sym14061271Google Scholar
  122. L. Ruppert et al. (2019). “Fading channel estimation for free-space continuous-variable secure quantum communication”. New Journal of Physics, 21: 12, 123036.DOI: 10.1088/1367-2630/ab5dd3Google Scholar
  123. R. Zhao, J. Zhou, R. Shi, and J. Shi, (2024). “Unidimensional continuous variable quantum key distribution under fast fading channel”. Annalen der Physik, 536: 5, 2300401.DOI: 10.1002/andp.202300401Google Scholar
  124. F. Yang, D. Qiu, and P. Mateus, (2023). “Continuous-variable quantum secret sharing in fast-fluctuating channels”. IEEE Transactions on Quantum Engineering, 4: 1–9.DOI: 10.1109/TQE.2023.3322171Google Scholar
  125. P. Papanastasiou, C. Weedbrook, and S. Pirandola, (2018). “Continuous-variable quantum key distribution in uniform fast-fading channels”. Physical Review A, 97: 3, 032311, doi: 10.1103/PhysRevA.97.032311.DOI: 10.1103/PhysRevA.97.032311Google Scholar
  126. S. Pirandola et al. (2015). “MDI-QKD: Continuous-versus discrete-variables at metropolitan distances”. arXiv preprint arXiv:1506.06748.Google Scholar
  127. P. Wang, X. Wang, and Y. Li, (2019). “Continuous-variable measurement-device-independent quantum key distribution using modulated squeezed states and optical amplifiers”. Physical Review A, 99: 4, 042309, doi: 10.1103/PhysRevA.99.042309.DOI: 10.1103/PhysRevA.99.042309Google Scholar
  128. E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, (2016). “Practical challenges in quantum key distribution”. npj Quantum Information, 2: 1, 1–12.DOI: 10.1038/npjqi.2016.25Google Scholar
  129. C. M. Knaut et al. (2024). “Entanglement of nanophotonic quantum memory nodes in a telecom network”. Nature, 629: 8012, 573–578.DOI: 10.1038/s41586-024-07252-zGoogle Scholar
  130. É. Dumur et al. (2021). “Quantum communication with itinerant surface acoustic wave phonons”. npj Quantum Information, 7: 1, 173.DOI: 10.1038/s41534-021-00511-1Google Scholar
  131. R. Yanagimoto, P. L. McMahon, E. Ng, T. Onodera, and H. Mabuchi, (2019). “Embedding entanglement generation within a measurement-feedback coherent Ising machine”. arXiv preprint arXiv:1906.04902.Google Scholar
  132. Y. Inui and Y. Yamamoto, (2020). “Entanglement and quantum discord in optically coupled coherent Ising machines”. Physical Review A, 102: 6, 062419.DOI: 10.1103/PhysRevA.102.062419Google Scholar