Tao Shen

Continuous-variable quantum key distribution (CV-QKD) provides a way for two remote participants called Alice and Bob to establish symmetric keys through an unsafe channel \cite{weedbrook2012gaussian,grosshans2003quantum}. Continuous-variable quantum key distribution (CV-QKD) based on commercial devices such as lasers and coherent detectors is moving towards practical. Experimental implementation of the CV-QKD systems using Gaussian-modulated coherent states (GMCS) has made significant progress recently \cite{zhang2019continuous}. At the mean time, the problems of performance degradation caused by imperfections of those experimental devices remain unsolved absolutely \cite{pirandola2020advances}. A non-orthogonal measurement angular error between quadrature components $X$ and $P$ from coherent detection is always ignored in the current experimental scheme. The optical phase shifter that constantly rotates the local oscillator phase is a necessity in continuous-variable quantum key distribution systems using heterodyne detection. In previous experimental implementations, the optical phase shifter is generally regarded as an ideal passive optical device that perfectly rotates the phase of the electromagnetic wave of $90^\circ$ \cite{wang2020high}. However,under the action of external force, the fibre is stretched or compressed within the elastic deformation range, and parameters such as the fibre change's geometrical size and refractive index change, thus causing the phase change of the transmitted signal in the fibre. Therefore, the phase shifter is somewhat susceptible to environmental changes and can hardly shift the phase by $90^\circ$ exactly Considering this, we propose a concrete interpretation of measurement angular error in practical systems and the corresponding entanglement-based description. Simultaneously, an estimation method of the measurement angular error and corresponding compensation scheme are demonstrated in some ways. We conclude that measurement angular error severely degrades the security, but the proposed calibration and compensation method can significantly help improve the performance of the practical CV-QKD systems. Undoubtedly, it is worth observing that our work is to strengthen practical security resulted from devices' imperfection.

Quantum key distribution (QKD) which enables the secure distribution of symmetric keys between two legitimate parties is of great importance in future network security [1, 2]. Access network that connects multiple end-users with one network backbone can be combined with QKD to build security for end-users in a scalable and cost-effective way. Access network can have upstream stream transmission direction and downstream transmission direction. For upstream transmission, signals are transmitted from the end-users optical network units (ONUs), combined at the optical distribution network (ODN), and then forwarded to the optical line terminal (OLT) through single fiber. For downstream transmission direction, signals are sent from the OLT and separated at the ODN, then distributed to ONUs in the network. Though previous QKD access network demonstrations are all based on upstream transmission direction [3], the downstream access network on the other hand may offer extra advantages, since no time multiplexing technique is applied, the crosstalk is minimized, also, only passive beam- splitter is sufficient to distribute the signals, and no active controls or calibrations are required at the intermediate optical distribution network node, signals are simply broadcasted to the ONUs [4]. However, it is not straight- forward to integrate QKD into the downstream access network, for discrete-variable QKD, the quantum signals cannot be deterministically distributed to the ONUs. More importantly, since every ONU gets a copy of the transmitted quantum signals, it is crucial that the final secret key is private against other ONUs in the downstream access network. Here, we prove that QKD downstream access network can be realized by using continuous-variable (CV) QKD [5], the corresponding implementation can deterministically perform QKD [6] with the activated ONU, the network still only applies passive beamsplitter to distribute quantum signals. The secrecy against other parties in the network is achieved by considering a reinforced Eve during the security analysis. The security analysis can be conducted with only the optical line terminal and the activated ONU, and no other parties assistances are required. Our work provides the security analysis framework for realizing QKD in the downstream access network which will boost the diversity for constructing practical QKD networks. This work was supported by the Key Program of National Natural Science Foundation of China under Grant No. 61531003, National Natural Science Foundation of China under Grant No. 62001041, China Postdoctoral Science Foundation under Grant No. 2020TQ0016, Sichuan Science and Technology Program under Grant No. 2020YFG0289 and the Fund of State Key Laboratory of Information Photonics and Optical Communications. [1] V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dusek, N. Lütkenhaus, and M. Peev, The security of practical quantum key distribution, Rev. Mod. Phys. 81, 1301 (2009). [2] 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). [3] B. Fr¨ohlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan and A. J. Shields, A quantum access network, Nature 501, 69-72 (2013). [4] ITU. G.984.1: Gigabit-capable passive optical networks (gpon): General characteristics. ITU-T (2008). [5] S. Pirandola, et al., Advances in quantum cryptography, Adv. in Opt. and Photon. 12, 1012 (2020). [6] Y. Zhang, et al., Continuous-variable QKD over 50km commercial fiber, Quantum Sci. Technol. 4, 035006 (2019).

Quantum key distribution (QKD) is designed to establish symmetric keys among two legitimate parties. Continuous variable (CV) QKD that uses the coherent states and homodyne detection can only apply the cost-effective telecommunication components[1]. The field test of CV-QKD has reached over 50 km[2], and under the laboratory conditions, experimental demonstration of over 200km has been reported [3], thus, has revealed great potentials in practical implementations. The access network that allows multitude end-users to connect to the nodal network is a necessary in the modern network infrastructure since it is suitable for general home-to-home scenarios. Quantum access network was first proposed [4] and demonstrated in field tests [5] for discrete variable QKD. Here, we report an upstream access network based on CV-QKD. In our experimental demonstrations, two transmitters Alice are deployed as optical network units that simultaneously send signals to the network, the receiver Bob is acted as the optical line terminal. The optical distribution network is located between the optical network units and the optical line terminal to couple the signals. The signals generated from each optical network unit are required to pass through a variable delay line to calibrate the arriving time at the optical distribution network before being transmitted. The signals are then simultaneously sent to the optical distribution network through fibers of 5.3 km and 12.3 km respectively. When the signals approach to the optical distribution network, dynamic polarization control modules are firstly applied in each path to pre-compensate the polarization. The signals are then coupled through a beamsplitter and forwarded to the optical line terminal. With a system repetition frequency of 2.5 MHz, we obtain the averaged secret key rates of 55 kbps and 22 kbps for Alice No. 1 and Alice No. 2 respectively. The total secret key rates has reached 77 kbps which suggests a higher network capacity. The excess noise is relatively stable, yet there are small fluctuations in the secret key rates. To one step further reduce the loss, the wavelength division multiplexing devices can be used at the optical distribution network. This is especially beneficial when the quantum signal has to co-propagate with classical data channels in the same fiber [6,7]. The upstream access network implementations can be easily extended to a higher repetition frequency system or to support more users. The demonstration experiments provide the possibility of building practical large-scale CV-QKD networks. This work is supported by the Key Program of National Natural Science Foundation of China under Grants No. 61531003, and the Fund of CETC under Grant No. 6141B08231115. References 1. C.Weedbrook, S. Pirandola, R. Garc´ıa-Patr´on, N. J. Cerf, T. C. Ralph, J. H. Shapiro and S. Lloyd, Gaussian quantum information, Rev. Mod. Phys. 84, 621 (2012). 2. Y. Zhang, Z. Li, Z. Chen, C. Weedbrook, Y. Zhao, X. Wang, Y. Huang, C. Xu, X. Zhang, Z. Wang, M. Li, X. Zhang, Z. Zheng, B. Chu, X. Gao, N. Meng,W. Cai, X.Wang, G.Wang, S. Yu and H. Guo, Continuous- variable QKD over 50 km commercial fiber, Quantum Sci. Technol. 4, 035006 (2019). 3. Y. Zhang, Z. Chen, S. Pirandola, X. Wang, C. Zhou, B. Chu, Y. Zhao, B. Xu, S. Yu and H. Guo, Long- distance continuous-variable quantum key distribution over 202.81 km fiber, arXiv:2001.02555 (2020). (Accepted by Phys. Rev. Lett.) 4. B. Fr¨ohlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan and A. J. Shields, A quantum access network, Nature 501, 69-72 (2013). 5. B. K. Park, M. K. Woo, Y. S. Kim, Y. W. Cho, S. Moon and S. W. Han, User-independent optical path length compensation scheme with sub-nanosecond timing resolution for a 1* N quantum key distribution network system, Photon. Res. 8, 296 (2020). 6. T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Lu´ıs, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada and M. Sasaki, Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 Tbit/s data channels, Commun. Phys. 2, 9 (2019). 7. B. Chu, Y. Zhang, Y. Zhao, Y. Xu, X. Chen, X. Wang and S. Yu, Crosstalk-induced impact of coexisting DWDM network on continuous-variable QKD, 16th International Conference on the Design of Reliable Communication Networks DRCN, Milano, Italy, pp. 1-5 (2020).