Time-bin Encoded Free-space QKD Experiment

Background

Quantum Key Distribution (QKD) enables unbreakable encryption by relying on the principles of quantum mechanics. While fiber-based QKD is already in advanced deployment in metropolitan networks, free-space QKD is essential for satellite-to-ground communication and for building the global quantum internet.

However, these two types of QKD use different technologies:

Fiber QKD uses:
- C-band infrared light (1550 nm) for low-loss in silica fibers.
- Time-bin encoding, as polarization can fluctuate in fibers.
Free-space QKD uses:
- Visible or near-infrared light for better beam divergence control.
- Polarization encoding, since it’s robust against atmospheric effects.

This creates a compatibility problem between ground-based fiber users and satellite-based free-space links.

What the Original Paper Tried to Achieve

Paper Title:
Time-bin encoding quantum key distribution in free-space horizontal links during nighttime and daytime
Authors: Sebastiano Cocchi et al.
arXiv: 2501.08891v1

Objective:

To demonstrate that time-bin encoding, typically used in fibers, can be reliably used in horizontal free-space channels, allowing direct interoperability between fiber networks and satellite free-space links using the same protocol and wavelength.

Key Highlights from the Paper:

Implemented time-bin QKD using a three-state BB84 protocol with one-decoy method.
Operated at C-band (1558.98 nm) using horizontal free-space links:
- One 50-meter link (lab-to-lab).
- One 500-meter link (museum-to-lab).
Achieved high key rates:
- 793 kbps over 50m.
- 40 kbps over 500m.
Used a photonic integrated circuit and adaptive optics (deformable mirrors) for beam stabilization.

Our Experiment – Replication with a Twist

We replicated this setup in a simulated open research lab environment, following all experimental design elements from the paper but with some crazy chnages. This tests the protocol’s robustness in worst-case optical loss conditions—useful for longer-range or deep-space QKD feasibility studies.

Experimental Setup Overview

Component	Description
Encoding Scheme	Time-bin encoding with 800 ps delay between bins using Intensity Modulator (IM)
Quantum Signal Laser	1558.98 nm (C-band), Weak Coherent Pulse Laser, 1680 ps pulse width
Synchronization Laser	1560.61 nm Clock Laser, 10 MHz (50 m), 145 kHz (500 m)
Beacon Laser	1310.1 nm for beam alignment
Pulse Rate	595 MHz pulse repetition (from laser), modulated at 1.2 GHz via FPGA
Time-bin Encoder	Intensity Modulator with ±12V driver, 800 ps delay
Attenuation	Fixed (55 dB) + VOA (15 dB) + Beam Splitter (20 dB) = Total: 90 dB
Photonic Integrated Circuit	Borosilicate-glass with ion-exchange waveguide, Peltier + PID stabilized
Measurement – X basis	PIC-based IMZI with 800 ps delay
Measurement – Z basis	Direct arrival time with SNSPD (efficiency: 90%)
Detectors	SNSPDs placed after IMZI and Beam Splitter
Receiver Optics	Galilean Telescope (Thorlabs GBE10-C, 10× mag, 35 mm lens)
Beam Alignment	Deformable Mirror + PID Controller (controlled using FQD)
Position Detector	Thorlabs PDQ30C (FQD) — 0.75 μm resolution, 3.05 mm depth
Signal Coupling	Fiber Collimator (Thorlabs C80APC-C), 15 mm beam diameter
Fiber Link	Single Mode Fiber from telescope to detection unit
Synchronization Recovery	Photodiode extracts clock from CS via DWDM and HFWDM
Wavelength Filtering	DWDM (1558.98 + 1560.61 nm), HFWDM (adds 1310.1 nm)
Clocking Electronics	FPGA (1 V output, 1.2 GHz), Driver Circuit (±12V swing to IM)
Time Tagging	Time Tagger digitizes detector clicks for analysis
Software Stack	Computes: QBER_X, QBER_Z, Visibility, Secure Key Rate (block size: 10⁷ pulses)

Mathematical Formulas Used

Secure Key Rate in Finite Key Regime:

\text{SKR} = R_{\text{sifted}} \cdot \left[1 - f_{\text{EC}} \cdot H_2(\text{QBER}_Z) - H_2(\text{QBER}_X)\right]

Where:

$H_2(p) = -p \log_2 p - (1 - p) \log_2(1 - p)$
Binary entropy function
$f_{\text{EC}} = 1.1$
Error correction inefficiency
QBER values come from measurement basis statistics.

All Component We have used

These components are created using VIEW AI (Research Assistant in ORL)

{
  "DWDM": {
    "type": "Dense Wavelength Division Multiplexer",
    "combined_wavelengths": [1558.98, 1560.61]
  },
  "HFWDM": {
    "type": "High-Frequency WDM",
    "combined_wavelengths": [1310.1, 1558.98, 1560.61]
  },
  "CW Laser": {
    "linewidth": "< 100 kHz",
    "wavelength": 1558.98
  },
  "Beacon Laser (BL)": {
    "type": "CW laser",
    "wavelength": 1310.1
  },
  "Clock Signal Laser (CS)": {
    "type": "SFP pulsed laser",
    "wavelength": 1560.61,
    "frequencies": {
      "50m_link": "10 MHz",
      "500m_link": "145 kHz"
    }
  },
  "FPGA Pulse Generator": {
    "frequency": 1.2,
    "signal_type": "Electrical drive for IM",
    "voltage_range": "+/-12V (amplified)"
  },
  "Driver Circuit": {
    "function": "Amplifies FPGA output to Vπ of IM",
    "input_voltage": 1,
    "output_voltage": "+/-12V"
  },
  "Intensity Modulator": {
    "type": "Amplitude Modulator",
    "delay": 800,
    "material": "Lithium Niobate"
  },
  "Fiber Collimator": {
    "model": "Thorlabs C80APC-C",
    "diameter_mm": 42.5,
    "output_beam_diameter_mm": 15
  },
  "Galilean Telescope": {
    "model": "Thorlabs GBE10-C",
    "magnification": 10,
    "lens_diameter_mm": 35
  },
  "Deformable Mirror (DFM)": {
    "type": "Tip-Tilt Mirror",
    "control": "Closed-loop PID",
    "correction": "Beam wandering"
  },
  "Dichroic Mirror (DM)": {
    "function": "Separates BL from QS/CS"
  },
  "Photodiode (PD)": {
    "function": "Clock extraction from CS",
    "placement": "After DWDM"
  },
  "Time-Tagger Unit": {
    "input": "Clock from PD",
    "function": "Assign timestamps to SNSPD clicks"
  },
  "Four-Quadrant Detector (FQD)": {
    "model": "Thorlabs PDQ30C",
    "depth_mm": 3.05,
    "function": "Track beacon laser position",
    "resolution_um": 0.75
  },
  "Fixed Attenuator": {
    "attenuation": "Static; part of 75 dB total attenuation"
  },
  "Variable Optical Attenuator": {
    "attenuation": "Adjustable",
    "integration": "Fiber-integrated",
    "max_attenuation": 75
  },
  "SNSPD Z-basis": {
    "type": "Superconducting Nanowire Detector",
    "connected_to": "First output port of BS"
  },
  "SNSPD X-basis": {
    "type": "Superconducting Nanowire Detector",
    "connected_to": "IMZI output"
  },
  "PIC Interferometer (IMZI)": {
    "delay_ps": 800,
    "material": "Borosilicate glass matrix",
    "integration": "Edge-coupled SMF",
    "stabilization": "Peltier + PID",
    "waveguide_tech": "Ion-exchange"
  },
  "Fiber Polarization Controller (FPC)": {
    "function": "Compensate for PIC polarization dependency"
  },
  "Beam Splitter (BS)": {
    "type": "50:50",
    "function": "Bob’s random basis choice"
  },
  "Single Mode Fiber (SMF)": {
    "function": "Captures aligned light from FS channel",
    "wavelength": 1550
  },
  "QKD Software": {
    "formula": "Efficient BB84 with one-decoy, finite-key regime",
    "block_size": 10000000,
    "calculates": [
      "QBER_Z",
      "QBER_X",
      "Visibility",
      "SKR"
    ]
  }
}

Results we got

{
  "loss_db": 90.0002,
  "scintillation_index": 0.0000040727,
  "QBER_Z": 0.0051,
  "QBER_X": 0.01,
  "Visibility": 0.98,
  "Secure_Key_Rate_per_Block": 0
}

Comparison with Real Experiment

Metric	Our Setup (90 dB)	Paper (50 m link)	Paper (500 m link)
Attenuation	90.0 dB	7 dB	16–17 dB
Raw Sifted Key Rate	Near 0 bps	~800 kbps	~40 kbps
Secure Key Rate	0 bps	709–793 kbps	35–40 kbps
QBER Z / X	0.51% / 1%	Low / Low	Low / Moderate
Visibility	98%	94%	85%
Num. of Pulses	10 million	Continuous	Continuous

Reason for Discrepancy

Despite decent QBER and visibility, our secure key rate is 0. Here’s why:

Factor	Impact
Extreme Attenuation (90 dB)	The photon arrival probability is drastically low, leading to very few detection events. Even with a 10 million pulse simulation, only a tiny fraction of signals are received — which is insufficient to generate sifted keys reliably.
Sifted Key Size Too Small	Finite-key security protocols require minimum detection thresholds to apply privacy amplification. With low detections, the statistical fluctuations dominate, nullifying the key rate.
Block Size Dependency	This setup uses a block size of `10⁷` pulses. At high losses, may need longer runtime or higher repetition rate to accumulate enough detections within a block.
Detector Timing + Dark Counts	Even with good visibility, timing jitter and background noise (dark counts) at very low signal levels can degrade effective SNR, contributing to 0 SKR.

Suggestions for Future Improvement

Reduce attenuation to values (e.g., < 70 dB) for good space-based scenarios.
Increase the number of simulation pulses beyond 10 million.
Consider using decoy-state analysis with adaptive block sizes for better SKR estimation under high loss.

Running This in Open Research Laboratory

To run this QKD experiment within the Open Research Laboratory, follow these steps:

Go to the Open Research Laboratory platform (or your deployed instance).
Click on the “Workflow” tab in the sidebar.
Find and click on the experiment titled:
“Time-bin Encoded Free-space QKD Experiment”
Click the “Enter Workflow” button on the right-hand side.
Once inside, you’ll see the preconfigured simulation pipeline with all components:
- Photon source
- Attenuation stage
- Interferometer (IMZI)
- Single-photon detectors
Click “Run Workflow” to start the simulation.
Results including QBER, SKR, and visibility will be displayed in the results panel.

💡 Tip: You can modify parameters like attenuation, visibility, or pulse rate before running, to explore how they impact the secure key rate.

Conclusion

Despite achieving low QBER and high visibility (indicating clean interference and good alignment), the secure key rate dropped to zero due to extremely high total loss (90 dB). This shows:

Time-bin encoding can survive under harsh conditions, but:
Detection probability becomes too low for a reliable key rate in extreme attenuation scenarios.
This aligns with the principles of finite-key security: if too few bits are received, no secret key can be distilled, regardless of quality.

Citation

Cocchi, S., Ribezzo, D., Guarda, G., Centorrino, P., Occhipinti, T., Zavatta, A., & Bacco, D. (2025). Time-bin encoding quantum key distribution in free-space horizontal links during nighttime and daytime. arXiv preprint arXiv:2501.08891v1. https://arxiv.org/abs/2501.08891