Sub-Gbps key rate four-state continuous-variable quantum key distribution within metropolitan area

Continuous-variable quantum key distribution (CVQKD) enables information-theoretic secure key sharing between Alice and Bob and is well-suited for broadband metropolitan and access networks due to potentially high key rates and compatibility with commercial components. Despite progress, experimentally reported CVQKD systems typically achieve only several Mbps secret key rates (SKRs), insufficient for high-speed one-time-pad applications. Two practical CVQKD modulation schemes exist: Gaussian-modulated coherent states (GMCS) and discrete-modulated coherent states (DMCS). While GMCS has advanced, high-rate GMCS demands DAC/ADC with high linearity over large amplitude ranges, limiting SKR. DMCS (e.g., four-state) offers practical advantages at low SNR and with lower linearity requirements across large bandwidths, potentially improving SKR. High-speed DMCS with a local local oscillator (LLO) avoids security loopholes and intensity limitations of a transmitted LO. However, achieving ultra-high SKR in DMCS LLO-CVQKD faces key challenges: (1) precise phase noise compensation between independent lasers and robust suppression of excess noises (photon leakage, modulation/detection, quantization) in large bandwidth; (2) prior SKR evaluations often use the linear channel assuming (LCA) method that restricts Eve’s attacks, motivating more general analyses secure against collective attacks (e.g., SDP); (3) lack of high-efficiency, high-throughput post-processing to extract final keys. This work addresses these issues and experimentally demonstrates a four-state DMCS LLO-CVQKD achieving sub-Gbps asymptotic SKR over metropolitan distances by engineering a low-noise transceiver, precise fast-slow phase noise compensation, and high-efficiency post-processing.

The paper contrasts GMCS and DMCS CVQKD. GMCS has seen substantial theoretical and experimental progress, but practical high-rate implementation is constrained by DAC/ADC linearity for Gaussian amplitudes. DMCS (e.g., four-state) is advantageous at low SNR and lower linearity requirements, aiding higher SKR. LLO-CVQKD eliminates transmitted-LO vulnerabilities and intensity constraints. Previous high-speed DMCS LLO-CVQKD works often evaluated SKR under LCA security models, restricting Eve’s strategies. More general analyses like user-defined methods and semidefinite programming (SDP) support collective attacks but demand very low tolerable excess noise (~0.01 SNU). Prior experiments also lacked highly efficient, high-speed post-processing pipelines, limiting practical SKR extraction. The authors position their work as overcoming these limitations to approach sub-Gbps asymptotic SKR.

Experimental setup: A continuous optical carrier at Alice is split into two paths. The upper path is modulated by QPSK at Rsym=5 GBaud using an IQ modulator (FUJITSU FTM7962EP). Digital signals are generated by a 30 GSa/s AWG (Keysight M8195A), with DAC amplitude set to 320 mV and shaped by a root-raised cosine filter (roll-off α=0.3). The modulated signal is attenuated to a four-state quantum signal with average photons per pulse ≈0.47 (quantum optical power −65.2 dBm at 193.5 THz). The lower path is attenuated to create an intense pilot tone. Polarization controllers (PC1–PC3) align polarizations for optimal IQ modulation and pilot/LO alignment. The upper carrier is frequency-shifted by f=3.5 GHz relative to the lower carrier, isolating quantum and pilot signals in frequency. Quantum signal and pilot are co-propagated over 1550 nm single-mode fiber (SMF) with orthogonal polarizations and different frequency bands. At Bob, a polarization beam splitter (PBS) and polarization synthesis analyzer (PSA, PSY-201) separate and correct polarization, then two balanced homodyne detectors (BHDs, Optilab BPR-23-M) separately detect quantum and pilot tones with independent LLOs. Alice’s and Bob’s lasers are independent free-running sources (NKT Photonic Basik E15). Outputs are digitized by an 8-bit, 40 GS/s oscilloscope (Keysight DSOV084A) for DSP and post-processing. Design rationale: Independent generation and separate paths for weak quantum signal and intense pilot reduce modulation noise and DAC quantization noise; frequency separation in co-fiber transmission eliminates photon-leakage noise; separate detection reduces detection noise and ADC quantization noise given finite dynamic range and resolution. Measured spectra confirm no crosstalk between bands. DSP and phase noise compensation (PNC): Dual-channel ADC captures BHD outputs. Pilot frequency ΔfAB is estimated (7.505 GHz); the desired quantum center frequency is ΔfAB−fs=4.005 GHz (with f=3.5 GHz). Quantum and pilot signals are band-pass filtered, orthogonally down-converted to baseband, quantum is matched filtered (RRC), pilot is narrowband low-pass filtered. Fast-drift phase ΔφAB(k) is recovered by sharing pilot phase; slow-drift phase Δφqa(k) due to fiber delay/disturbance is adaptively recovered using an LMS filter (51 taps, step 1e−3). Symbol synchronization and precise laser wavelength control further improve recovery; adaptive filtering mitigates small optical-frequency deviations. Constellation diagrams at 25 km show clear improvement after PNC. Post-processing: Given low SNR, reverse reconciliation uses multidimensional reconciliation to produce binary sequences, followed by error correction using MET-LDPC codes. Three parity-check matrices tailored for 5, 10, and 25 km (code rates 0.07, 0.06, 0.03) are designed via 10-bit quantization density evolution to achieve target convergence thresholds and reconciliation efficiencies. Layered LDPC decoding and adaptive decoding are implemented on GPU (NVIDIA TITAN Xp). Privacy amplification uses Toeplitz matrices. Achieved threshold reconciliation efficiency βc ≈96–97% and rate-adaptive efficiency βr ≈95% across distances; SNRs around 0.119 (5 km), 0.094 (10 km), 0.047 (25 km). Security analysis and parameter choices: SKR is evaluated under both LCA and SDP security models. Simulations of SKR vs. excess noise and modulation variance at 25 km identify an optimal VA≈0.45 SNU; experiments use VA=0.456 SNU. Excess noise modeling considers laser intensity noise εRIN, DAC quantization εDAC, modulation εMod, photon leakage εLE, detection εDet, ADC quantization εADC, and phase noise εPhase (fast and slow). With trusted-receiver assumptions (BHD and ADC), εDet and εADC are treated as trusted noise in LCA and ignored (η=1, va=0) in SDP. Key parameters/estimates: εRIN≈8.1×10−5; εDAC≈4.64×10−4; εMod≈4.7×10−4 (IQ extinction 40 dB; quantum power −65.2 dBm); εLE eliminated via frequency separation; εDet (theory)≈0.2714 SNU for r=0.2 ns, B=6.5 GHz, NEP=5.8 pW/√Hz, PLO=4 dBm; εADC≈0.0101 SNU (Cg=1500 V/W, Rv=120 mV, n=8); measured electronic noise va≈0.297 (theory 0.2815). Fast-drift laser phase noise is negligible with <0.1 kHz linewidth; PNC reduces phase noise with residual Ephase_rest≈0.0032 SNU (pilot compensation error ≈0.0022; LMS error ≈0.001). An additional “other noise” term ≈0.0033 SNU is attributed to setup instabilities (e.g., IQ bias drift, polarization correction non-idealities). Total excess noise excluding trusted electronic noise at 25 km is ≈0.0075 SNU.

- Demonstrated a four-state DMCS LLO-CVQKD system achieving sub-Gbps asymptotic key rates over metropolitan distances with ultra-low excess noise and high reconciliation efficiency. - Achieved asymptotic SKRs: LCA method: 190.54 Mbps (5 km), 133.6 Mbps (10 km), 52.48 Mbps (25 km). SDP method: 233.87 Mbps (5 km), 137.76 Mbps (10 km), 21.53 Mbps (25 km). - Symbol rate: 5 GBaud; modulation variance VA=0.456 SNU selected near optimal. - Measured mean excess noise (trusted-receiver model, excluding trusted electronic noise) across distances: ~0.0072 (5 km), 0.0073 (10 km), 0.0075 (25 km) SNU. - Excess noise thresholds for null SKR: SDP: 0.0176 (5 km), 0.0141 (10 km), 0.0092 (25 km); LCA: 0.0563 (5 km), 0.0497 (10 km), 0.0371 (25 km). - Reconciliation performance: threshold βc≈96.5–97.5%; achieved rate-adaptive βr≈95–95.5% at SNRs ≈0.119 (5 km), 0.094 (10 km), 0.047 (25 km). - Noise budget at 25 km (SNU): εRIN≈8.1×10−5; εDAC≈4.64×10−4; εMod≈4.7×10−4; residual phase noise ≈0.0032; other noise ≈0.0033; detection noise (trusted) ≈0.2869; ADC quantization (trusted) ≈0.0101; total excess noise excluding trusted ≈0.0075. - System architecture (frequency- and polarization-multiplexed independent pilot and quantum paths, separate BHDs, precise fast-slow PNC) effectively suppresses modulation, quantization, detection, photon-leakage, and phase noises, enabling performance sufficient for one-time-pad applications within metropolitan scales.

The study addresses the practical challenge of achieving ultra-high SKR CVQKD suitable for metropolitan networks. By independently generating and frequency/polarization multiplexing the weak quantum signal and intense pilot, and separately detecting them, the system mitigates modulation, quantization, detection, and photon-leakage noises. The precise pilot-assisted fast-drift and LMS-based slow-drift phase recovery reduces phase noise to a residual ~0.0032 SNU, enabling operation under the stringent excess-noise tolerance required by the SDP security model. The chosen modulation variance near 0.45 SNU maximizes SKR under both LCA and SDP analyses. Experimental mean excess noises (~0.0072–0.0075 SNU) are well below the SDP null-SKR thresholds at 5–25 km, yielding high asymptotic SKRs and validating the system’s coherence and noise control. The high-efficiency, rate-adaptive MET-LDPC-based reconciliation (β≈95%) further translates raw correlations into final keys at high rates. Compared with prior works, the combination of 5 GBaud symbol rate, ultra-low excess noise, and efficient post-processing significantly boosts SKR, demonstrating the feasibility of sub-Gbps asymptotic rates in single-carrier four-state LLO-CVQKD. These results support practical high-speed QKD deployment for broadband metropolitan/access networks and show that general collective-attack security (via SDP) can be realized experimentally when excess noise is sufficiently suppressed.

The work experimentally demonstrates a four-state discretely modulated LLO-CVQKD system achieving sub-Gbps asymptotic secret key rates over 5–25 km metropolitan distances. Independent generation and frequency/polarization multiplexing of quantum and pilot signals with separate detection reduce multiple noise sources, while a precise fast-slow phase noise compensation scheme achieves ultra-low excess noise at 5 GBaud. A high-efficiency, rate-adaptive post-processing pipeline (β>95%) successfully extracts final keys offline. Achieved asymptotic SKRs are 233.87/190.54 Mbps (SDP/LCA) at 5 km, 137.76/133.6 Mbps at 10 km, and 21.53/52.48 Mbps at 25 km. The study is the first to evaluate a high-rate experimental DMCS CVQKD setup under an SDP framework resistant to general collective attacks, paving the way for practical high-rate metropolitan QKD and one-time-pad applications. Future work will focus on real-time post-processing, enhancing coherent stability, extending to larger constellations or Gaussian modulation, and incorporating tight finite-size security analyses.

- Post-processing was performed offline; real-time reconciliation and privacy amplification at the demonstrated rates remain to be implemented. - Security evaluation in SDP is asymptotic; finite-size secure key rates under four-state CVQKD with tight finite-size proofs were not reported. - The SDP method tolerates very low excess noise, requiring stringent noise suppression; operational margins may be tight in field environments. - Trusted-receiver assumptions (BHD and ADC) are used in LCA analysis; any deviations from trust could impact security and SKR estimates. - Potential side-channel leakage from IQ modulation sidebands requires careful filtering in practical deployments. - Setup stability issues (e.g., IQ bias drift, polarization control) contributed to residual “other” noise (~0.0033 SNU); long-term field stability needs further work. - Distances tested up to 25 km; performance over longer spans or higher losses not characterized here.