In this paper, we study the theory of four-wave mixing type noises over multicore fiber (MCF) and analyze the impacts of the noises on quantum key distribution (QKD) in the quantum and classical coexistence system. The models about four-wave mixing type noises proposed in this paper include forward inter-core four-wave mixing (FIC-FWM), backward four-wave mixing (B-FWM) and backward inter-core four-wave mixing (BIC-FWM). a) The model of FIC-FWM based on discrete change model (FIC-FWM-DCM) is proposed to obtain the precise power of FIC-FWM. Simultaneously, we further propose the model of FIC-FWM based on extended coupled-power theory (FIC-FWM-ECPT) which can obtain similar results to FIC-FWM-DCM but with lower computational complexity. b) The generation mechanism of B-FWM is proposed, and the model is built by combining forward four-wave mixing and backward Rayleigh scattering. c) The generation mechanism of BIC-FWM is proposed, and the model is built by combining FIC-FWM and B-FWM. Based on the above three models of four-wave mixing type noises, we analyze the impacts of the noises on QKD in the quantum and classical coexistence systems over MCF. The results show that the proposed models of FIC-FWM can significantly improve the simulation accuracy in the coexistence system. B-FWM noise can generate a serious impact on QKD when the guard bandwidth between quantum and classical channels is less than 250 GHz with the launch power of 2 mW. BIC-FWM noise can generate a significant impact on QKD when the frequency spacing is less than or equal to 25 GHz and the launch power is larger than 2 mW. Finally, the experiments are carried out to measure FIC-FWM, and the results show the proposed model of FIC-FWM can obtain the consistent results with experiments.
In this paper, we study the theory of four-wave mixing type noises over multicore fiber (MCF) and analyze the impacts of the noises on quantum key distribution (QKD) in the quantum and classical coexistence system. The models about four-wave mixing type noises proposed in this paper include forward inter-core four-wave mixing (FIC-FWM), backward four-wave mixing (B-FWM) and backward inter-core four-wave mixing (BIC-FWM). a) The model of FIC-FWM based on discrete change model (FIC-FWM-DCM) is proposed to obtain the precise power of FIC-FWM. Simultaneously, we further propose the model of FIC-FWM based on extended coupled-power theory (FIC-FWM-ECPT) which can obtain similar results to FIC-FWM-DCM but with lower computational complexity. b) The generation mechanism of B-FWM is proposed, and the model is built by combining forward four-wave mixing and backward Rayleigh scattering. c) The generation mechanism of BIC-FWM is proposed, and the model is built by combining FIC-FWM and B-FWM. Based on the above three models of four-wave mixing type noises, we analyze the impacts of the noises on QKD in the quantum and classical coexistence systems over MCF. The results show that the proposed models of FIC-FWM can significantly improve the simulation accuracy in the coexistence system. B-FWM noise can generate a serious impact on QKD when the guard bandwidth between quantum and classical channels is less than 250 GHz with the launch power of 2 mW. BIC-FWM noise can generate a significant impact on QKD when the frequency spacing is less than or equal to 25 GHz and the launch power is larger than 2 mW. Finally, the experiments are carried out to measure FIC-FWM, and the results show the proposed model of FIC-FWM can obtain the consistent results with experiments.
In the quantum and classical coexistence system, the classical noises can affect the performance of quantum key distribution (QKD). Among these noises, forward intercore four-wave mixing (FIC-FWM) noise has a serious impact. However, the current analytical theories of FIC-FWM are not yet fully developed. In this paper, we derive an analytical equation for FIC-FWM based on correlation functions (termed FICFWM-CF). The FIC-FWM-CF model can be applied in both homogeneous and heterogeneous multicore fibers (MCFs) with low computational complexity. Then, we analyze the effect of FIC-FWM noise on QKD performance in the quantum and classical coexistence system, revealing that frequency spacings should exceed 75 GHz for homogeneous MCFs and 50 GHz for heterogeneous MCFs to effectively mitigate FIC-FWM noise interference. Finally, we experimentally investigate the impact of FIC-FWM noise on QKD and demonstrate that the FIC-FWMCF model can accurately predict the resulting trends in QKD performance.
In this paper, the influence of noise induced by classical signals on independent core transmitting quantum key distribution (QKD) is studied over multicore fiber (MCF). We propose a theoretical model of the cascaded noise of spontaneous Raman scattering and inter-core crosstalk (SpRS-ICXT), and the cascaded noise of four-wave mixing and inter-core crosstalk (FWM-ICXT) considering modulation frequency over MCF. To analyze the effect of modulation frequency on QKD, we define and simulate the average power difference and power fluctuation difference of SpRS-ICXT and FWM-ICXT. Then, SpRS-ICXT and FWM-ICXT noises are simulated in two cases: (1) 1 or 3 classical channels and 1 km MCF; (2) 8 or 16 classical channels and 45 km MCF. For the latter case, SpRS-ICXT and FWM-ICXT noises have a serious impact on QKD. Therefore, the impact of noise on QKD is studied. A higher modulation frequency can improve QKD performance, and the secure transmission distance can be further extended by 15.2% when the modulation frequency is 10 GHz relative to ignoring the modulation frequency. However, inter-core crosstalk (ICXT), SpRS-ICXT and FWM-ICXT noises will shorten 52.2% secure transmission distance compared to only transmitting QKD. Finally, the noise of quantum channel is experimentally measured at different symbol rates and modulation formats of classical signals, and it is shown that increasing the symbol rate of data signals at the same optical power degrades the secure key rate of QKD system.
In this paper, we propose core and wavelength allocation schemes for the simultaneous transmission of classical signals and quantum key distribution (QKD) over multi-core fiber (MCF), aiming to maximize the secure key rate, and evaluate the proposed schemes in sending-or-not-sending-QKD (SNS-QKD) and Bennett-Brassard-1984-QKD (BB84-QKD). First, we formulate the noise power on quantum channels, and propose a theoretical model of backward cascaded noise of four wave mixing and inter-core crosstalk considering modulation frequency of the classical signals. Also, the impact of noises on secure key rate is calculated in SNS-QKD and BB84-QKD. Then, we propose a core allocation algorithm in order to reduce the noise interference to quantum cores, and the quantum equal frequency spacing (qEFS) and the quantum unequal frequency spacing (qUFS) wavelength allocation schemes are proposed in the same-core (SC) and the different-core (DC) distribution. Finally, we perform numerical simulation and experimental evaluation for the proposed schemes. Compared with the conventional channel allocation (CCA) scheme in SNS-QKD, the proposed schemes can extend the secure transmission distance up to 78.8%. In BB84-QKD, the secure transmission distance can be extended up to 127.1% under SC-qUFS scheme. Experimental results show that the proposed schemes can suppress noise photons up to 57.54% compared to CCA scheme.
In this paper, we investigate the impact of classical optical communications in quantum key distribution (QKD) over hollow-core fiber (HCF), multi-core fiber (MCF) and single-core fiber (SCF) and propose wavelength allocation schemes to enhance QKD performance. Firstly, we theoretically analyze noise interference in QKD over HCF, MCF and SCF, such as spontaneous Raman scattering (SpRS) and four-wave mixing (FWM). To mitigate these noise types and optimize QKD performance, we propose a joint noise suppression wavelength allocation (JSWA) scheme. FWM noise suppression wavelength allocation and Raman noise suppression wavelength allocation are also proposed for comparison. The JSWA scheme indicates a significant enhancement in extending the simultaneous transmission distance of classical signals and QKD, reaching approximately 100 km in HCF and 165 km in MCF under a classical power per channel of 10 dBm. Therefore, MCF offers a longer secure transmission distance compared with HCF when classical signals and QKD coexist in the C-band. However, when classical signals are in the C-band and QKD operates in the O-band, the performance of QKD in HCF surpasses that in MCF. This research establishes technical foundations for the design and deployment of QKD optical networks.
Mitigating inter-core crosstalk is critical for the coexistence of classical optical signals and continuous-variable quantum key distribution (CV-QKD) in multi-core fibers (MCFs). In this work, a comprehensive excess-noise model is developed for MCF-based classical/CV-QKD coexistence, including direct inter-core crosstalk (ICXT), SpRS-ICXT, FWM-ICXT, and XPM-induced phase noise. Based on this model, we analyze the effects of classical launch power, channel spacing, inter-core coupling coefficient, and modulation variance on the secure key rate and total excess noise. A constrained optimization of classical launch power, channel spacing, and modulation variance is further performed under classical-link feasibility requirements, including receiver sensitivity, received-power margin, and implementation loss. The results show that ICXT is the dominant impairment under the considered MCF conditions, and that the optimized configuration achieves higher SKR and longer secure reach than fixed baseline settings while maintaining classical-channel availability. This work provides a theoretical noise-modeling and constrained-optimization framework for practical classical/CV-QKD coexistence in MCFs.
In this paper, the influence of classical signals on quantum key distribution (QKD) is studied over multi-core fiber (MCF) when optical amplifiers exist. Firstly, the long-distance simultaneous transmission architectures of QKD and classical signals are proposed based on advanced asymmetric sending or not sending QKD (SNS-QKD) and classical Bennett-Brassard 1984-QKD (BB84-QKD), and the segment length between optical amplifiers can be adjusted according to requirement. Then, theoretical models of spontaneous Raman scattering noise and four-wave mixing noise are established based on the proposed architectures. Next, the calculation models of the secure key rate under the influence of noises from classical signals are derived. Finally, the experimental results show that the theoretical models match well with the experimental photons, and the maximum difference between experimental and simulated noise photons is less than 2.6 dB. Simulation results show that the performance of asymmetric SNS-QKD is better than that of BB84-QKD architecture when classical signals and quantum signals are transmitted in different cores of MCF.