Smart Photonic and Optoelectronic Integrated Circuits
Limits of phase recovery in CV-QKD systems: an experimental analysis
Maria H. F. Silva, Christiano M. S. Nascimento, Artur A. Matoso, Davi Juvêncio Gomes de Sousa, Nelson Alves Ferreira Neto, David M. C. Bezerra, Maron F. Anka, Felippe A. S. Barbosa, Guilherme P. Temporão, Gustavo Castro do Amaral, Braian P. Silva, Alexandre B. Tacla, Valeria L. Silva
Phase recovery is a key enabling process in continuous-variable quantum key distribution (CV-QKD) systems operating at ultra-low optical power, where phase noise from the finite linewidths of the transmitter and local oscillator lasers critically impacts system performance. Here, we investigate the performance of a phase recovery scheme for a prepare-and-measure CV-QKD setup using the Viterbi–Viterbi carrier phase estimation algorithm. We experimentally evaluate the scheme by varying the power of a binary phase shift keying (BPSK)-modulated pilot tone, using laser sources with nominal linewidths of 1 kHz and 25 kHz. Our results reveal a well-defined operational regime in which stable phase recovery is achieved, as well as a critical threshold below which pilot tone power becomes insufficient, leading to signal distortion and phase recovery failure. As expected, narrower-linewidth lasers exhibit improved phase stability and reduced variance, confirming the combined impact of pilot tone power and laser linewidth on phase recovery performance. These findings provide practical guidelines for CV-QKD receiver synchronization.
Phase recovery is a key enabling process in continuous-variable quantum key distribution (CV-QKD) systems operating at ultra-low optical power, where phase noise from the finite linewidths of the transmitter and local oscillator lasers critically impacts system performance. Here, we investigate the performance of a phase recovery scheme for a prepare-and-measure CV-QKD setup using the Viterbi–Viterbi carrier phase estimation algorithm. We experimentally evaluate the scheme by varying the power of a binary phase shift keying (BPSK)-modulated pilot tone, using laser sources with nominal linewidths of 1 kHz and 25 kHz. Our results reveal a well-defined operational regime in which stable phase recovery is achieved, as well as a critical threshold below which pilot tone power becomes insufficient, leading to signal distortion and phase recovery failure. As expected, narrower-linewidth lasers exhibit improved phase stability and reduced variance, confirming the combined impact of pilot tone power and laser linewidth on phase recovery performance. These findings provide practical guidelines for CV-QKD receiver synchronization.
Continuous-variable quantum key distribution (CV-QKD) has been increasingly studied, which offers the advantage of compatibility with modern coherent optical communication systems. In contrast to CV-QKD with a transmitting local oscillator, the local local oscillator CV-QKD avoids the security vulnerabilities of a local oscillator by generating a local oscillator at the receiver. In practice, the frequency offset of the two lasers introduces extra phase noise, which is generally suppressed by various carrier phase recovery algorithms. However, the accuracy of carrier phase recovery can be influenced by the power of the pilot tone, particularly as the transmission distance increases. To further improve accuracy, we propose a method based on the unscented particle filter algorithm, to increase the accuracy of phase estimation, effectively restore the quantum signal and reduce excess noise. In our work, we demonstrated a local local oscillator CV-QKD experiment with a finite-size block of 1×108 under a transmission distance of 50 km. Through our method, we achieved a secret key rate of 525 kbps, which represents a 28% improvement. These results confirm that our proposed method not only improves the accuracy of carrier phase recovery, but also provides a new approach for future research on algorithms for long-distance CV-QKD. Furthermore, our study improves the phase compensation performance, enabling the orthogonal components of the quantum signal to exhibit enhanced symmetry in phase space.
Continuous-Variable Quantum Key Distribution (CV-QKD) offers practical advantages for secure communication, but laser linewidth-induced phase noise remains a critical performance limitation. This work presents a comprehensive simulation-based analysis quantifying the impact of laser linewidth on secret key rate (SKR) in Gaussian-modulated coherent-state CV-QKD systems. We develop a detailed noise model incorporating detector electronics, Raman scattering, phase recovery, ADC quantization, and laser relative intensity noise. Through systematic parameter sweeps spanning linewidths from 10 Hz to 250 kHz, modulation variances from 1 to 20 SNU, and fiber distances up to 100 km, we identify three distinct operational regimes and optimization strategies for both transmitted local oscillator (TLO) and local–local oscillator (LLO) configurations under homodyne and heterodyne detection. Results show that metropolitan-scale links (50 km) require linewidths below 5 kHz to maintain secure operation, with performance decreasing beyond 25 kHz. We demonstrate that modulation variance must be jointly optimized with laser quality, with optimal values decreasing from 3–4 SNU at narrow linewidths to 2–2.5 SNU at moderate linewidths. The analysis reveals asymmetric sensitivity in LLO systems where local oscillator linewidth degrades performance more strongly than signal laser linewidth. These quantitative findings provide practical design guidelines for achieving secure CV-QKD operation over metropolitan distances with realistic hardware constraints, supporting deployment of defense-grade quantum communication networks.
Abstract The secret key rate of a continuous-variable quantum key distribution (CV-QKD) system is limited by excess noise. A key issue typical to all modern CV-QKD systems implemented with a reference or pilot signal and an independent local oscillator is controlling the excess noise generated from the frequency and phase noise accrued by the transmitter and receiver. Therefore accurate phase estimation and compensation, so-called carrier recovery, is a critical subsystem of CV-QKD. Here, we explore the implementation of a machine learning framework based on Bayesian inference, namely an unscented Kalman filter (UKF), for estimation of phase noise and compare it to a standard reference method and a previously demonstrated machine learning method. Experimental results obtained over a 20-km fibre-optic link indicate that the UKF can ensure very low excess noise even at low pilot powers. The measurements exhibited low variance and high stability in excess noise over a wide range of pilot signal to noise ratios. This may enable CV-QKD systems with low hardware implementation complexity which can seamlessly work on diverse transmission lines.
The simultaneous quantum and classical communication (SQCC) protocol is an appealing protocol since it allows continuous-variable quantum key distribution (CV-QKD) and classical communication to be implemented simultaneously by using the same communication infrastructure and on a single wavelength. However, the main challenge of the SQCC protocol is its low tolerance of phase noise, limiting the transmission distance under the real local oscillator (LO) design. To eliminate the phase drift without the aid of the reference signal, the classical carrier phase estimation (CPE) algorithm in the field of coherent optical communication is employed for phase recovery and data extraction. Besides, the power of the residual phase noise in classical communication and the power of the excess phase noise in CV-QKD are derived, including the effects of the employed laser linewidth, the transversal filter length, and the classical signal power. On this basis, the performances of the SQCC protocol under the trusted and the untrusted phase noise model are discussed, respectively. Our work confirms the feasibility of the CPE algorithm in the SQCC protocol and demonstrates the conditions required for this protocol to operate on a coherent optical communication system.
The performance of local local oscillator-based continuous-variable quantum key distribution (LLO-CVQKD) systems is critically limited by phase recovery accuracy. To address the phase mismatch between independently operated lasers at the transmitter and receiver, this work proposes a multi-pilot scheme integrated with advanced digital filtering for optimized phase estimation. Through systematic comparisons of the rectangular filter, Savitzky-Golay filter, and Wiener filter, experimental results confirm that Wiener filtering has superior noise suppression capabilities based on multiple frequency pilot-tones. Implemented under the Gaussian-modulated coherent state (GMCS) protocol, our findings reveal that dual-pilot, four-pilot, and eight-pilot configurations all enhance phase recovery precision compared to single-pilot approaches, with the dual-pilot scheme achieving optimal balance between system complexity and performance. In a 20 km fiber link with a 1 GHz system repetition rate and a 2.83 SNU modulation variance, the dual-pilot Wiener-filtered configuration achieves an asymptotic secret key rate of almost 80 Mbps, establishing an innovative approach for practical LLO-CVQKD phase recovery.
Quantum key distribution (QKD) enables information-theoretic-secure secret key exchange thanks to the laws of quantum mechanics. Since it can easily be incorporated into existing telecom networks, continuous-variable QKD (CV QKD) using coherent states and coherent detection has recently emerged as a promising candidate. However, the secret key rate and link distance in CV QKD systems are still limited by the imperfections of used components. In this work, through simulations, we study the use of different digital filtering techniques for optical phase recovery, aided by pilot symbols, to mitigate the phase noise induced by the coherent mixing of two free-running lasers in a CV QKD system. Moving average, Butterworth and unscented Kalman filters are evaluated for different phase drift conditions. Results show that phase recovery from small amplitude pilot symbols, along with further digital filtering, can considerably reduce phase noise and measurement error, while increasing the secret key rate and link distance of the CV QKD system.