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

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.

💡 Research Summary

This paper addresses a critical gap between the high‑speed continuous‑variable quantum key distribution (CV‑QKD) systems enabled by modern digital signal processing (DSP) and the existing security proofs, which are limited to static DSP algorithms. In practical dual‑polarization CV‑QKD, time‑varying channel impairments such as state‑of‑polarization drift, polarization‑dependent loss (PDL), and phase rotation are compensated by dynamic multiple‑input multiple‑output (MIMO) DSP algorithms. The authors demonstrate that the conventional dynamic MIMO (C‑MIMO) algorithm is intrinsically non‑unitary when PDL is present, causing systematic mis‑estimation of the excess noise. If the scaling factors of the equalizer matrix exceed unity, the estimated noise variance becomes larger than the true value, leading to an overly pessimistic key rate; if they are below unity, the excess noise is underestimated, potentially allowing an eavesdropper to obtain information without detection.

To resolve this, the authors propose a quantum‑aware MIMO (Q‑MIMO) model that maps the digital equalizer operation onto an equivalent physical optical network whose security can be rigorously analyzed. The key steps are: (1) perform singular‑value decomposition (SVD) of the equalizer matrix W, yielding W = U Ω Vᵀ, where U and V are unitary (polarization rotations) and Ω is a diagonal scaling matrix containing the singular values ωₓ and ω_y. (2) Recognize that non‑unitary scaling corresponds to either a beam‑splitter (attenuation) or a phase‑insensitive amplifier (gain) in the quantum optical domain. (3) Introduce trusted Gaussian noise in the digital domain that mimics the vacuum noise added by these physical components: for attenuation, add q·(1 − ω²)·N_D; for gain, add q·(ω² − 1)·N_D, where N_D has unit variance and q is a calibrated factor. (4) Normalize the matrix by its largest singular value ω_max so that the resulting matrix W′ = W/ω_max always represents a pure attenuation (0 ≤ ω′ₓ, ω′_y ≤ 1) and can be modeled as a beam‑splitter followed by trusted noise. The final Q‑MIMO output is therefore expressed as
S_Q_out = √T·α_A + U