Quantum Encryption Secured Against Hacking with New Digital Signal Processing Technique

Researchers have demonstrated a significant advance in practical continuous-variable quantum key distribution, addressing a critical flaw in current security assessments. Lu Fan, Zhengyu Li, and Sheng Liu from the China Mobile Research Institute, alongside Xuesong Xu, Tianyu Zhang from Beijing University of Posts and Telecommunications, and Jiale Mi, reveal that standard dynamic digital signal processing algorithms systematically underestimate excess noise, potentially compromising key security. Their work establishes a novel algorithm model, linking dynamic processing to a physically assessable optical system, and provides both simulated and experimental evidence of this underestimation.

This research achieves a secure key rate of 14.4 Mbps with an excess noise of 0.07 shot noise units, a result sharply contrasting with the dangerously inflated 28.2 Mbps rate predicted by conventional algorithms, thereby offering an essential framework for developing robust, high-performance quantum communication systems. Existing security proofs for CV-QKD have been limited to static algorithms, while practical, high-speed systems rely on dynamic multiple-input multiple-output (MIMO) algorithms to counteract the effects of fluctuating channel conditions. This work reveals that conventional dynamic algorithms, due to their non-unitary nature, systematically underestimate excess noise, potentially leading to insecure key generation. To address this fundamental issue, researchers propose a secure algorithm model that maps the dynamic algorithm to an equivalent physical optical model, enabling rigorous security assessment. Simulations demonstrate the non-unitary properties of the conventional algorithm and quantify the resulting underestimation of excess noise. Experimental validation confirms the necessity of this new modeling approach for dynamic digital signal processing, achieving a secret key rate of 14.4 Mbps with an estimated excess noise of 0.07 shot noise unit. In contrast, the conventional algorithm dangerously overestimated the key rate at 28.2 Mbps, while reporting a significantly lower noise level of 0.008 shot noise unit.

This research establishes an essential security framework for dynamic digital signal processing, removing a major obstacle to the development of high-performance CV-QKD systems. The study details a system employing digital signal processing to enhance the performance of CV-QKD, leveraging both training sequences for channel response acquisition and quantum sequences for key information transmission. Static DSP algorithms address hardware imperfections, including square root raised cosine filtering for inter-symbol interference and compensation for non-flat frequency responses using S21 parameters. Dynamic MIMO equalization specifically targets time-varying polarization impairments, such as drift in the state of polarization and polarization dependent loss. Researchers employed SVD decomposition to demonstrate that the proposed quantum MIMO (Q-MIMO) compensation can be represented by physically describable matrices. Further analysis models Q-MIMO as a combination of passive linear optical networks and a beam splitter/phase insensitive amplifier model, allowing for rigorous security assessment. The experimental setup utilized a 25.3km fiber channel, where the implementation of the Q-MIMO method yielded a secure key rate of 14.4 Mbps. This advancement paves the way for integrating quantum and classical signals on the same fiber, potentially enabling transmission capacities of 100G/200G and beyond, and facilitating network routing and slicing capabilities. Dynamic channel estimation and compensation for continuous-variable quantum key distribution A 25.3km fiber channel served as the experimental platform for validating a new modeling approach to dynamic digital signal processing. Researchers implemented a continuous-variable quantum key distribution system employing digital signal processing to mitigate time-varying channel impairments. The core of the methodology involved characterizing and compensating for dynamic multiple-input multiple-output channel effects, specifically those arising from polarization drift and polarization dependent loss. A training sequence with slightly higher power was first used to acquire the channel response for damage compensation, without constraints on its digital signal processing algorithm. Subsequently, the quantum sequence containing key information underwent processing with a focus on security considerations. The system utilized a balanced homodyne detector, coupled with an analog-to-digital converter and a digital storage oscilloscope for signal acquisition. Static equalization techniques, including SRRC matched filtering and inverse transfer function filtering, addressed static hardware imperfections and inter-symbol interference. These algorithms relied on precise prior knowledge of the impairment model for single-detection channels. Dynamic MIMO equalization was then employed to counteract varying fiber impairments causing inter-channel crosstalk. The channel’s dynamic evolution was modeled using Jones matrices, recursively updated to reflect polarization rotation, polarization dependent loss, and phase shifts. The instantaneous channel response was calculated at each time step, building upon the previous state and a small rotation matrix. An adaptive filter, trained using the least mean square algorithm, was implemented to estimate the inverse of the channel response. The filter matrix was dynamically updated by minimizing the mean square error between the equalizer output and the original transmitted signal. This work achieved a secret key rate of 14.4 Mbps, based on an estimated excess noise of 0.07 shot noise unit, demonstrating the necessity of the proposed modeling for dynamic digital signal processing. Experimental demonstration of secure continuous-variable quantum key distribution via noise characterisation A secret key rate of 14.4 Mbps was experimentally achieved using a proposed quantum multiple-input multiple-output algorithm on a 25.3km fiber channel. This performance was based on an estimated excess noise of 0.07 shot noise unit, demonstrating a functional continuous-variable key distribution system. Conversely, a conventional dynamic algorithm overestimated the key rate to 28.2 Mbps, calculating noise at only 0.008 shot noise unit, highlighting a significant security vulnerability. The research addresses a critical gap in existing proofs of continuous-variable key distribution, which previously lacked analysis of dynamic digital signal processing algorithms. Simulations clearly illustrate the non-unitary property of the conventional dynamic algorithm, revealing a systematic underestimation of excess noise. Quantitative analysis demonstrates the extent of this underestimation, providing a detailed understanding of the resulting insecurity. The proposed algorithm model maps the dynamic algorithm to an equivalent physical optical model, enabling rigorous security assessment. This framework overcomes a critical impediment to developing high-performance continuous-variable key distribution systems. The study details the use of digital signal processing to reduce hardware complexity and improve transmission capacity by suppressing noise in digital CV-QKD systems. Two types of sequences are employed: a higher-power training sequence for channel response acquisition and a quantum sequence containing key information, requiring careful security considerations. Static equalization techniques, such as square root raised cosine matched filtering and I/Q imbalance correction, compensate for static hardware imperfections. Dynamic multiple-input multiple-output equalization addresses time-varying fiber impairments like birefringence and polarization dependent loss. The channel matrix evolves recursively, with the instantaneous response at time k derived from the previous state and an incremental evolution matrix. Adaptive filtering, exemplified by the least mean square algorithm, trains a transmission matrix to operate on the received signal, ideally functioning as the inverse of the channel response. The trained matrix compensates for attenuation and crosstalk in additive Gaussian white noise channels, but the non-unitary nature of this compensation necessitates further security analysis for quantum signals. Non-unitary effects in dynamic CV-QKD and secure key rate validation Researchers have established a framework for accurately modelling dynamic digital signal processing algorithms used in continuous-variable key distribution systems. Existing security proofs for these systems were limited to static algorithms, while practical implementations employ dynamic multiple-input multiple-output algorithms to mitigate time-varying channel impairments. This work addresses a critical gap by demonstrating that conventional dynamic algorithms underestimate excess noise due to their non-unitary nature, potentially leading to insecure key generation. The investigation introduces a novel algorithm model that maps dynamic algorithms to an equivalent physical optical model, enabling rigorous security assessment. Simulations confirmed the non-unitary properties of the conventional algorithm and quantified the resulting underestimation of excess noise. Experimental validation, conducted over a 25.3km fibre channel, achieved a secure key rate of 14.4 Mbps using the proposed modelling approach, based on an estimated excess noise of 0.07 shot noise units. In contrast, the conventional algorithm would have falsely indicated a key rate of 28.2 Mbps with a dangerously low noise estimate of 0.008 shot noise units.

This research overcomes a significant impediment to developing high-performance continuous-variable key distribution systems by providing an essential framework for dynamic digital signal processing. The authors acknowledge that their model relies on accurate characterisation of the dynamic channel evolution, and limitations in this characterisation could affect the precision of the security analysis. Future research directions include exploring the application of this modelling framework to more complex dynamic algorithms and investigating its performance under more realistic channel conditions, potentially incorporating feedback mechanisms to further refine noise estimation and enhance key rates. 👉 More information 🗞 Practical continuous-variable quantum key distribution using dynamic digital signal processing: security proof and experimental demonstration 🧠 ArXiv: https://arxiv.org/abs/2602.05206 Tags: