Analyzing the performance of CV-MDI QKD under continuous-mode scenarios

TL;DR

The paper tackles performance limits of CV-MDI QKD under continuous-mode interference caused by spectrum broadening in high-speed operation. By introducing temporal modes (TM) and TM-based matching coefficients, it develops PM and EB descriptions that account for realistic broadband spectra and detector responses. It shows that mismatches between Bob's TM and the Bell measurement TM critically degrade both maximum transmission distance and secret-key rate, with 5% Bob mismatch collapsing distance from 87.96 km to 18.50 km and causing large rate losses at shorter distances; Alice's TM mismatch has a comparatively smaller effect. Finite-size analysis indicates these impacts persist under practical data lengths, underscoring the need for rigorous pre-calibration of TM characteristics in future large-scale MDI networks. The TM framework thus offers practical guidance for designing and optimizing continuous-mode CV-MDI QKD implementations.

Abstract

Continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) can address vulnerabilities on the detection side of a QKD system. The core of this protocol involves continuous-variable Bell measurements performed by an untrusted third party. However, in high-speed systems, spectrum broadening causes Bell measurements to deviate from the ideal single-mode scenario, resulting in mode mismatches, reduced performance, and compromised security. Here, we introduce temporal modes (TMs) to analyze the performance of CV-MDI QKD under continuous-mode scenarios. The mismatch between Bob's transmitting mode and Bell measurement mode has a more significant effect on system performance compared to that on Alice's side. When the Bell receiver is close to Bob and the mismatch is set to just 5%, the transmission distance drastically decreases from 87.96 km to 18.50 km. In comparison, the same mismatch for Alice reduces the distance to 86.83 km. This greater degradation on Bob's side can be attributed to the asymmetry in the data modification step. Furthermore, the mismatch in TM characteristics leads to a significant reduction in the secret key rate by 83% when the transmission distance is set to 15 km, which severely limits the practical usability of the protocol over specific distances. These results indicate that in scenarios involving continuous-mode interference, such as large-scale MDI network setups, careful consideration of each user's TM characteristics is crucial. Rigorous pre-calibration of these modes is essential to ensure the system's reliability and efficiency.

Figures (6)

• Figure 1: (a) PM model of CV-MDI under a single-mode scenario. (b) PM model of CV-MDI under a continuous-mode scenario. (c) The preparation of a continuous-mode Gaussian-modulated coherent state in the EB model is equivalent to performing heterodyne detection on one mode of a continuous-mode TMSV. (d) Data correction in the PM model is equivalent to displacement operations in the EB model. Mode-matching coefficients between the measured state's TM and the detector's TM is necessary under the continuous-mode scenario.
• Figure 2: Equivalent one-way model of the EB scheme.
• Figure 3: (a) Symmetric structure of CV-MDI QKD. (b)Charlie placed at Alice's side. Black line represents the ideal single-mode case; green line represents $\eta_{\mathrm{m}}^{\mathrm{A}}=0.95$ and $\eta_{\mathrm{m}}^{\mathrm{B}}=1$; blue line represents $\eta_{\mathrm{m}}^{\mathrm{A}}=1$ and $\eta_{\mathrm{m}}^{\mathrm{B}}=0.95$; red line represents $\eta_{\mathrm{m}}^{\mathrm{A}}=\eta_{\mathrm{m}}^{\mathrm{B}}=0.95$.
• Figure 4: Extremely asymmetric structure with Charlie placed at Bob's side. The dashed lines represent the results considering finite-size effects with a code length of $N=10^{8}$. Black line represents the ideal single-mode case; green line represents $\eta_{\mathrm{m}}^{\mathrm{A}} =0.95$ and $\eta_{\mathrm{m}}^{\mathrm{B}}=1$; blue line represents $\eta_{\mathrm{m}}^{\mathrm{A}}=1$ and $\eta_{\mathrm{m}}^{\mathrm{B}}=0.95$; red line represents $\eta_{\mathrm{m}}^{\mathrm{A}}=\eta_{\mathrm{m}}^{\mathrm{B}}=0.95$.
• Figure 5: The secret key rate varies with changes in $\eta_{\mathrm{m}}^{\mathrm{A}}$ and $\eta_{\mathrm{m}}^{\mathrm{B}}$ at a fixed distance (15km).