Quantum key distribution and 1 Gbit/s data encryption over a single fibre

Patrick Eraerds; Nino Walenta; Matthieu Legre; Nicolas Gisin; Hugo Zbinden

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Quantum key distribution and 1 Gbit/s data encryption over a single fibre

Patrick Eraerds, Nino Walenta, Matthieu Legre, Nicolas Gisin, Hugo Zbinden

arXiv:0912.1798v1Dec 9, 2009quant-ph

TL;DR

The paper asks whether QKD and encrypted communication can share a single dedicated fibre despite noise from co-propagating classical channels. It implements a commercial QKD system with four C-band DWDM classical channels, demonstrates secret-key generation to 50 km, and evaluates alternative configurations and improvements.

Problem
QKD traditionally required separate fibres for the weak quantum channel and classical key distillation or encrypted communication, motivating compatibility with single-fibre infrastructure.
Method
The authors multiplex the quantum channel, four classical channels, key distillation, and encrypted communication in a C-band DWDM configuration, while modeling and measuring relevant noise sources.
Results
Secret keys are obtained over 50 km, including 11 bps at 50 km with SARG, while the single-fibre system remains comparable to the two-fibre configuration up to 25 km.
Takeaways & Limitations
A commercial QKD encryption system can operate on one dedicated fibre with moderate additional efforts, without requiring another network connection.
Takeaways & Limitations
The current setup has little room for further Raman-noise reduction through narrower filtering, and improved receiver sensitivity beyond 3 dB is considered unlikely soon.

Abstract

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We perform quantum key distribution (QKD) in the presence of 4 classical channels in a C-band dense wavelength division multiplexing (DWDM) configuration using a commercial QKD system. The classical channels are used for key distillation and 1 Gbps encrypted communication, rendering the entire system independent from any other communication channel than a single dedicated fibre. We successfully distil secret keys over fibre spans of up to 50 km. The separation between quantum channel and nearest classical channel is only 200 GHz, while the classical channels are all separated by 100 GHz. In addition to that we discuss possible improvements and alternative configurations, for instance whether it is advantageous to choose the quantum channel at 1310 nm or to opt for a pure C-band configuration.

I. INTRODUCTION

The paper addresses operating QKD alongside classical communication on one fibre, avoiding the traditional two-fibre arrangement. It investigates a single-fibre DWDM system carrying quantum, key-distillation, and encrypted-communication channels.

Traditional QKD systems used a dedicated dark fibre for the quantum channel and a second fibre for classical key distillation and encrypted communication.
Existing DWDM infrastructure can multiplex many wavelengths, but classical signals may severely degrade or prevent QKD through crosstalk, Raman scattering, four-wave mixing, and amplified spontaneous emission.
A single dedicated fibre is desirable because it improves availability and reduces fibre leasing costs.
The proposed configuration carries all system-relevant channels on one fibre and enables direct performance characterization with known classical-channel conditions.
The experiment multiplexes four classical channels and one quantum channel using 100 GHz DWDM spacing, with 200 GHz separation between the quantum and nearest classical channel.

A. Raman scattering

The paper characterizes Raman scattering as a broadband wavelength-shifting noise source and uses measured fibre scattering to calculate forward and backward Raman power and detector-gate contributions.

A. Raman scattering: Photon–phonon interactions generate Stokes and anti-Stokes photons that can compromise other wavelength channels.Brillouin scattering is considered noncritical because its maximum backward frequency shift is only 10 GHz.
A. Raman scattering: Optical-phonon dispersion produces a broad scattered-photon spectrum in both co-propagating and counter-propagating directions.
A. Raman scattering: Measured Raman scatter from 50 km of standard single-mode fibre yields an effective cross-section ρ(λ) normalized by spectral bandwidth and fibre length.The cross-section accounts for the fibre capture ratio of scattered light.
A. Raman scattering: The measured cross-section and fibre attenuation determine backward Raman power Pram,b and forward Raman power Pram,f.The resulting Raman contributions are expressed as detection probabilities per ns detector gate.
A. Raman scattering: The Raman model uses output laser power, attenuation coefficient, and fibre length, with Pout = Pin · e−α·L.Equal attenuation for the initial and scattered wavelengths is assumed across the 4 nm total wavelength span.

B. Channel crosstalk

Channel crosstalk is evaluated against detector dark counts using receiver sensitivity, DWDM isolation, and Raman contributions; the reported 82 dB isolation is sufficient for the stated setup.

B. Channel crosstalk: The required DWDM isolation is set by the classical channels’ relative strength and the transceiver sensitivity needed for error-free detection.The benchmark is based on a receiver sensitivity guaranteeing BER < 10−12.
B. Channel crosstalk: An isolation of about 80 dB reduces classical-channel photons to a detection probability comparable to the 5·10−6 ns−1 detector dark-count probability.The estimate uses -28 dBm receiver sensitivity, approximately 1.2 · 104 photons per ns, and η = 0.07 with 2.65 dB internal loss.
B. Channel crosstalk: Figure 3 combines the relevant noise contributions using 82 dB DWDM isolation, 0.21 dB/km fibre loss, four −28 dBm classical channels, η = 0.07, and 2.65 dB internal loss.
B. Channel crosstalk: 82 dB isolation between non-adjacent channels is just sufficient to meet the stated dark-count benchmark.Additional filters can improve isolation but increase insertion loss in the quantum channel.
B. Channel crosstalk: Raman-scattering crosstalk is not a limiting factor for long fibre lengths in the considered configuration.
B. Channel crosstalk: Sufficient isolation between co-propagating quantum and classical channels allows Rayleigh-backscatter crosstalk in the counter-propagating configuration to be neglected.

C. Four-wave mixing

The paper examines four-wave mixing as a nonlinear source of additional photon frequencies, distinguishing stimulated generation from spontaneous signal–idler creation.

C. Four-wave mixing: Four-wave mixing is mediated by the third-order susceptibility χ(3) and generates photon frequencies absent from the initial fields.The process transfers no energy to or from the fibre because it involves no phonon excitation or de-excitation.
C. Four-wave mixing: The most harmful stimulated case considered is degenerate four-wave mixing, where two exciting frequencies generate sidebands.
C. Four-wave mixing: Spontaneous four-wave mixing creates signal and idler frequencies satisfying 2fp = fs + fi, with efficient generation governed by phase matching.Near the zero-dispersion wavelength, the generated spectrum can be broad and overlap Raman-scattering noise.

A. Setup

The system combines QKD, key distillation, and bidirectional 1 Gbps AES-256 encryption over one fibre by multiplexing the quantum and classical channels in a C-band DWDM configuration.

QKD and encryption hardware: A commercial Cerberis system combines point-to-point QKD with Layer 2 encryption units for secure bidirectional communication.The QKD layer uses plug-and-play phase encoding with passive compensation of optical and mechanical fluctuations.
Quantum layer: Bob generates 5 MHz optical pulses, and InGaAs APDs detect the quantum signals in Geiger mode.The APDs use 1.5 ns gates, 10 µs dead time, approximately 0.07 detection efficiency, and dark count probability near 5 · 10^-6 ns^-1.
Channel configuration: Four classical channels support bidirectional key distillation and encrypted data transmission alongside the quantum channel.Two authenticated channels serve distillation, while two channels serve bidirectional encrypted communication.
Wavelength configuration: The quantum channel uses 1551.72 nm, with classical channels placed at higher wavelengths and separated from it by 200 GHz.The configuration omits the adjacent channel to combine lower Raman noise with higher non-adjacent-channel isolation.
Noise mitigation: Classical channel powers are attenuated to match the receiver sensitivity of -28 dBm, while optional fibre Bragg grating filters reject 85% of noise photons.Each filter has 45 pm bandwidth, 14 dB extinction ratio, and 2 dB insertion loss.
Measurement configurations: The experimental data use BB84 and SARG key sifting with and without spectral filters to evaluate secret key rate and QBER.Table I reports the measured Rsec and QBER values for these configurations.

B. Results

Performance is evaluated through QBER and net secret key rate versus fibre length, with filtering and SARG sifting extending the operating range. The measurements and calculations agree well, while filter stability remains a practical constraint.

Distance performance: Additional filtering extends the maximum fibre length to 41 km with BB84 and 50 km with SARG.Figure 5 compares experimental symbols with calculated solid lines for QBER and secret key rate.
Operating thresholds: The system requires QBER below 9% for secret-key distillation and at least 8.6 bps for AES-256 keys refreshed once per minute.The calculated rates overestimate performance because key-distillation and fibre-length measurement times are omitted, especially at short distances.
BB84 results: At 35 km, spectral filtering raises the BB84 secret key rate from 4.3 bps to 25 bps.With filtering, BB84 reaches 7.5 bps at 41 km.
SARG results: At 35 km, SARG provides an average secret key rate of 128 bps and delivers 11 bps at 50 km.The passage states that SARG equally guarantees the security of the key material.
Unfiltered results: Without spectral filters, BB84 maintains a secret key rate above 1000 bps up to 10 km.This is the measured unfiltered short-distance performance.
Stability: With filters installed, one detector maintains a constant detection rate, but the second decreases after several hours because of filter-spectrum drift.The drift is attributed most likely to a filter fabrication flaw.

IV. DISCUSSION AND OUTLOOK

The discussion evaluates alternative wavelength choices, higher-rate encrypted channels, and prospective QKD systems for improving single-fibre DWDM performance. The analysis finds no benefit from moving the quantum channel to 1310 nm, limited impact from 10 Gbps channels at shorter distances, and substantially improved projections for a COW prototype.

Alternative wavelength configurations: 1310 nm Raman noise is about 4000 times weaker than at 1550 nm, but the combined O-band/C-band configuration does not improve performance.The comparison uses SARG with filters and assumes fibre attenuations of 0.21 dB/km at 1550 nm and 0.35 dB/km at 1310 nm.
Higher-rate encrypted channels: A 3.2 dB increase in classical power from 10 Gbps transceivers causes no significant secret-key-rate degradation up to 40 km.The estimate keeps all other parameters unchanged and uses transceivers with receiver sensitivity of -23 dBm instead of -28 dBm.
Higher-rate encrypted channels: The maximum distance for achieving a key rate of 8.6 bps decreases by 4–5 km with 10 Gbps encrypted channels, depending on the sifting protocol.
Performance improvements: Further filtering offers no practical improvement because the 45 pm spectral filter already limits the sub-nanosecond quantum-signal bandwidth.Narrower temporal filtering would clip pulses and introduce additional losses, while narrower temporal and spectral filtering trade off through pulse bandwidth.
Prospective QKD systems: A COW prototype projection reaches 70 km maximum link distance and more than 10,000 bps for fibre lengths up to 43 km.The estimate assumes a 312.5 MHz encoding frequency and mean photon number µ_COW = 0.5 photons per pulse.

V. CONCLUSIONS

The experiment demonstrates that a commercial QKD-based encryption system can operate over one dedicated fibre, multiplexing the quantum and classical channels together. Secret keys are obtained over spans up to 50 km, with only a moderate rate reduction relative to a two-fibre dark-fibre configuration at shorter distances.

50 km is the demonstrated maximum fibre span for efficiently operating the QKD-based encryption system on one dedicated fibre.All four classical channels needed for the encrypted link are multiplexed with the quantum signal in a 100 GHz DWDM configuration.
Less than 50% is the secret-key-rate decrease up to 25 km relative to the conventional two-fibre dark-fibre configuration.

A. Derivation of Raman Scatter power formulas

The paper derives Raman-scatter detection probabilities and incorporates them with detector imperfections, visibility, and protocol parameters into QBER and secret-key-rate calculations.

A. Derivation of Raman Scatter power formulas: dPram(λ, x) models Raman-scatter power from a fibre element using launched power, attenuation, spectral cross-section, bandwidth, and element length.The fibre element is located at position x and has length dx.
A. Derivation of Raman Scatter power formulas: The approximately isotropic scatter must be propagated through fibre attenuation in both forward and backward directions over the full fibre length.The resulting integrations determine contributions emerging at the fibre output and input.
A. Derivation of Raman Scatter power formulas: pram,f and pram,b convert forward and backward Raman powers into detection probabilities per detector gate for QBER calculations.The conversion uses gate duration Δtgate and detector efficiency η; backward detection follows by replacing Pram,f with Pram,b.
B. Explicit QBER and key rate formulas: QBER is defined as false detections divided by total detections, with protocol-dependent β terms distinguishing BB84 and SARG.The expression includes signal, dark-count, afterpulse, Raman, and crosstalk detection probabilities.
B. Explicit QBER and key rate formulas: Every detection probability per detector gate contributes to the QBER expression, including pµ, pdc, pAP, pram, and pct.pµ depends on average photons per pulse, fibre transmission, detector efficiency, and Bob’s internal loss; the optimal µ depends on the sifting protocol.
B. Explicit QBER and key rate formulas: Rsift estimates the sifted-bit rate from detection probabilities, pulse repetition frequency frep, and duty-cycle factor ηduty.The expression includes β · pµ, detector noise terms, Raman and crosstalk detections, and ηduty.
B. Explicit QBER and key rate formulas: IAB is reduced below 1 by quantum bit errors, while error correction and privacy amplification reduce Rsift by the factor IAB − IAE.IAB and IAE denote mutual information per bit between Alice and Bob and between Alice and a potential eavesdropper.
B. Explicit QBER and key rate formulas: The key-rate correction uses the binary entropy H(p), while CASCADE consumes about 20 % more bits than the Shannon-limit ideal.The implementation therefore requires a corrected error-correction efficiency parameter ηCascade.