Cecilia Clivati

Twin-Field Quantum Key Distribution (TF-QKD) is an innovative family of protocols characterized by a weaker dependence of the achievable secret key rate on the channel loss, with respect to conventional QKD solutions. In this work, we discuss several important aspects encountered in TF-QKD when transitioning from point-to-point links to a network configuration. 1) The effects of path length mismatch between the two arms of the link (A-C and B-C) is discussed in several configurations. 2) The noise contributions (stronger in in-field deployment) are meticulously analyzed, their effect on the final key rate is estimated and solutions to mitigate the problem are implemented. 3) The topic of building complex and large networks with TF-QKD is tackled to find advantageous configurations. Interconnected macro-star networks based on TF-QKD are simulated by means of the “qkdnetsim” package of the network simulator “ns3”. The upcoming deployment of national QKD networks requires dedicated studies in this direction to build efficient and long-range solutions, compatible with current telecom standards.

Quantum key distribution (QKD) ensures the sharing of secret cryptographic keys between distant entities (typically called Alice and Bob), whose intrinsic security is guaranteed by the laws of nature [1–3]. Besides pioneering experiments involving satellite transmission [4], the challenge is the integration of this technology in telecommunication fiber networks, in particular in long haul segments [5–11]. The longest achievable communication distance is limited by the channel loss which increases exponentially with the fiber length and noise in the deployed single photon detector. The secure QKD key rate decreases exponentially with the channel fiber length. Although the communication distance could be extended using quantum repeaters, the related research is still at a proof-of-principle level [12]. Presently the widely adopted solution is the exploitation of trusted nodes, whose security represents however a significant technical issue. An innovative approach that overcomes, at least partially, the need for trusted node is represented by the recently proposed QKD protocol dubbed twin-field QKD (TF-QKD) [13]. In TF-QKD, the information is encoded on dim laser pulses generated at distant Alice and Bob terminals and sent through optical fiber over half of the entire communication distance to the central node, Charlie, where they interfere. For this reason, the TF-QKD has weaker dependence on channel losses, essentially doubling the communication distance with respect to the conventional prepare-and-measure QKD solution. TF-QKDhas been proved secure against general attacks (see e.g. [14–18]), but its implementation is challenging as the optical pulses sent by Alice and Bob are required to be phase-coherent and preserve coherence when reaching Charlie after travelling the long fiber paths. While phase coherence can be achieved by phase-locking the two QKD lasers in Alice and Bob to a common reference laser transmitted through a service channel, uncorrelated phase changes due to the length and refractive index fluctuations in the long optical fibers still remain and will reduce the visibility of the interference measurement. In the TF-QKD proof-of-principle experiments [19–26], this effect was mitigated by interleaving the QKD frames with classical transmission frames that were used to periodically realign the phases of interfering pulses. Here we present an alternative solution derived from the metrological research community, more precisely from atomic clocks comparison technology. Specifically, transmission of coherent laser radiation over thousand-kilometer-long fibers is exploited for the comparison of distant atomic clocks at the highest accuracy [27–32]. In this case phase fluctuations in long fiber also need to be addressed, othewise they would substantially degrade the comparison results. Precise comparison among these atomic clocks are made possible by the use of ultra-stable lasers and the active cancellation of the noise introduced by connecting fibers. Here we demonstrate that this technique can be successfully adapted into a TF-QKD setup. More specifically, we designed and developed an apparatus suitable for actively cancelling phase fluctuations of both the lasers and of the connecting fibers in a TF-QKD setup. This is achieved by transmitting an additional sensing laser light at a slightly different wavelength in the same fiber as the QKD dim pulses. In Charlie, this sensing laser is used for the fiber optical length stabilisation. We show that this multiplexed solution can be properly tuned in order to avoid a sizeable impact on the number of background photons observed by the single-photon detectors in the QKD channels, allowing simultaneous key streaming and channels stabilization, ensuring longer duty-cycles of the QKD process and a tighter control of the optical phase on long-haul deployed fibers. Furthermore, we tested our solution in a real-world network where the net losses between Alice and Bob are as high as 65 dB, resulting here in a distance of 206 km, or equivalent at 325 km on a fiber haul at common nominal losses of 0.2 dB/km [33]. References [1] Bennett, C. H. & Brassard, G. Quantum cryptography: public key distribution and coin tossing. Theor. Comput. Sci. 560, 7–11 (2014). [2] Scarani, V. et al. The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301 (2009). [3] Kwong Lo, H., Curty, M. & Tamaki, K. Secure quantum key distribution. Nature Photonics 8, 595-604 (2014). [4] Liao, S-K., Cai, W-Q., Pan, J-W. Satellite-to-ground quantum key distribution, Nature 549, 43-47 (2017) [5] Peev, M. et al. The SECOQC quantum key distribution network in Vienna, New J. Phys. 11, 075001 (2009). [6] Sasaki, M. et al. Field test of quantum key distribution in the Tokyo QKD Network. Opt. Expr. 19, 10387 (2011). [7] Dynes, J. F. et al. Cambridge quantum network. npj Quantum Inf. 5, 101 (2019). [8] Shimizu K., et al. Performance of long-distance quantum key distribution over 90-km optical links installed in a field environment of Tokyo metropolitan area. J. Lightwave Technol. 32,, 141-51 (2014). [9] Bacco, D. et al. Field trial of a three-state quantum key distribution scheme in the Florence metropolitan area. EPJ Quantum Technol.6, 5 (2019). [10] Choi, I. et al. Field trial of a quantum secured 10 Gb/s DWDM transmission system over a single installed fiber. Opt. Expr 22, 23121-23128 (2014). [11] Dixon, A. R. et al. Quantum key distribution with hacking countermeasures and long term field trial, Sci. Rep. 7, 7583 (2017). [12] Xu, F., Ma, X., Zhang, Q., Lo, H-K. & Pan, J-W. Secure quantum key distribution with realistic devices. Rev. Mod. Phys. 92, 025002 (2020) [13] Lucamarini, M., Yuan, Z. L., Dynes, J. F., Shields, A. J. Overcoming the rate-distance limit of quantum key distribution without quantum repeaters. Nature 557, 400-403 (2018). [14] Ma, X. Zeng, P., & Zhou, H. Phase-Matching Quantum Key Distribution. Phys. Rev. X 8, 031043 (2018). [15] Wang, X-B., Yu, Z-W. & Hu, X-L. Twin-field quantum key distribution with large misalignment error. Phys. Rev. A 98, 062323 (2018). [16] Lin J. & Lutkenhaus, N. Simple security analysis of phase-matching measurement-device-independent quantum key distribution. Phys. Rev. A 98, 042332 (2018); [17] Curty, M., Azuma, K. & Lo, H.-K. Simple security proof of twin-field type quantum key distribution protocol. npj Quantum Inf. 5, 64 (2019) [18] Yin, H-L. & Chen, Z-B. Finite-key analysis for twin-field quantum key distribution with composable security, Sci Rep. 9, 17113 (2019). [19] Wang, S. et al. Beating the Fundamental Rate-Distance Limit in a Proof-of-Principle Quantum Key Distribution System. Phys. Rev. X 9, 021046 (2019) [20] Minder, M. et al. Experimental quantum key distribution beyond the repeaterless secret key capacity. Nature Photon. 13, 334-338 (2019) [21] X. Zhong, Hu, J., Curty, M., Qian, L. & Lo, H-K. Proof-of-Principle Experimental Demonstration of Twin-Field Type Quantum Key Distribution. Phys. Rev. Lett. 123, 100506 (2019) [22] Chen, J-P. et al. Sending-or-Not-Sending with Independent Lasers: Secure Twin-Field Quantum Key Distribution over 509 km. Phys. Rev. Lett. 124, 070501 (2020). [23] Fang, X-T., et al. Implementation of quantum key distribution surpassing the linear rate transmittance bound. Nature Photon 14, 422-425 (2020). [24] Pittaluga M, et al., 600 km repeater-like quantum communications with dual-band stabilisation, arXiv:2012.15099 (2020) [25] Hui Liu et al., Field Test of Twin-Field Quantum Key Distribution through Sending-or-Not-Sending over 428 km, arXiv:2101.00276 (2021) [26] Jiu-Peng Chen et al., Twin-Field Quantum Key Distribution over 511 km Optical Fiber Linking two Distant Metropolitans, arXiv:2102.00433 (2021) [27] Clivati, C. et al. Optical frequency transfer over submarine fiber links. Optica 5, 893 (2018). [28] Clivati, C. et al. Common-clock very long baseline interferometry using a coherent optical fiber link. Optica 7, 1031-1037 (2020) [29] Grotti, J. et al. Geodesy and metrology with a transportable optical clock. Nature Physics 14, 437-441 (2018). [30] Lisdat, C. et al. A clock network for geodesy and fundamental science. Nat.Comm. 7, 12443 (2016). [31] Delva, P. et al. Test of Special Relativity Using a Fiber Network of Optical Clocks, Phys. Rev. Lett. 118, 221102 (2017). [32] Guena, J. First international comparison of fountain primary frequency standards via a long distance optical fiber link. Metrologia 54, 348 (2017). [33] Clivati, C. et al. Coherent phase transfer for real-world twin-field quantum key distribution, arXiv:2012.15199 (2021)