Practical continuous-variable quantum key distribution using dynamic digital signal processing: security proof and experimental demonstration

TL;DR

The paper addresses security risks in CV-QKD introduced by dynamic DSP in dual-polarization channels, where non-unitary MIMO can bias excess-noise assessments. It introduces the Q-MIMO model, mapping dynamic MIMO to an equivalent physical EB model via singular value decomposition and injecting trusted noise to maintain security, accompanied by a formal security analysis and simulations. Experimental validation on a 25.3 km fiber link yields 14.4 Mbps secret-key rate with Q-MIMO (0.07 SNU excess noise), while conventional C-MIMO would misrepresent security with artificially low noise estimates. This work provides a security framework for dynamic DSP in CV-QKD, enabling software-defined polarization compensation and enabling scalable, high-rate implementations.

Abstract

Digital signal processing technology has paved the way for the realization of high-speed continuous-variable quantum key distribution systems. However, existing security proofs are limited to static digital signal processing algorithms, while practical systems rely on dynamic multiple-input multiple-output algorithms to compensate for time-varying channel impairments. Our analysis reveals that the conventional dynamic algorithm, due to its non-unitary nature, systematically underestimates the excess noise, which in turn leads to security issues and the generation of insecure keys. To close this gap, we propose a secure algorithm model, mapping the dynamic algorithm to an equivalent physical optical model whose security can be rigorously assessed. Simulations illustrate the algorithm's non-unitary property and provide a quantitative analysis of the excess noise underestimation caused by the conventional algorithm. We further experimentally validate the necessity of the proposed modeling for dynamic digital signal processing, achieving a secret key rate of 14.4 Mbps based on estimated excess noise of 0.07 shot noise unit; whereas the conventional algorithm would have dangerously overestimated the key rate to 28.2 Mbps with noise of 0.008 shot noise unit. This work provides the essential security framework for dynamic digital signal processing, overcoming a critical impediment for the development of high-performance continuous-variable quantum key distribution systems.

Figures (8)

• Figure 1: The hardware architecture for the CV-QKD system and corresponding DSP compensation algorithms. SRRC, square root raised cosine; AWG, arbitrary waveform generato; BHD, balanced homodyne detector; BPF, band-pass filter; DSO, digital storage oscilloscope; ADC, analog to digital converter; LMS, least mean square; CMA, constant modulus algorithm.
• Figure 2: The dynamic evolution model of generalized channel. The dual-polarization input signal $S_A$ is transformed into the output signal $S_B$ through the optical channel $J_{ch}$. The instantaneous channel response at point $k$ is recursively derived from the previous state $J_{ch}^k$ and the incremental evolution matrix $\Delta J^k$ where $\Delta J^k$ accounts for polarization rotation, PDL and phase shift.
• Figure 3: The training process of LMS equalization algorithm. The filter matrix $W$ is dynamically updated based on the error between the equalizer output and the original signal .
• Figure 4: (a) The practical architecture of hardware and softwore within the CV-QKD receiver. PBS, polarization beam splitter. (b) The full EB model of DSP algorithm for CV-QKD. In the first stage, the static DSP is modeled as MF. In the second stage, the dynamic 1Q-MIMO is modeled as three equivalent physical operations. PDCR, polarization diversity coherent receiver. MF, mode-filter
• Figure 5: (a) The singular value of the MIMO non-unitary in X-Pol and X-Pol. (b) The difference curve between the two singular values of (a). (c) The real-time underestimation of excess noise. (d) The statistical integral average of excess noise variation of (c).