High-Dimensional Quantum Key Distribution via full Core-mode Encoding over Deployed Multicore Fibers

This paper demonstrates the first high-dimensional quantum key distribution protocol over a deployed multicore fiber network that fully utilizes all available core modes for encoding, achieving a record-breaking per-pulse secret-key rate of $6.19\times 10^{-3}$ bits under realistic environmental conditions.

The Gist

Imagine you are trying to send a secret message to a friend across a busy city. In the world of quantum cryptography, this is called Quantum Key Distribution (QKD). It's a way to create a secret code that is mathematically impossible to crack because it relies on the laws of physics, not just complex math.

For a long time, these secret messages were like sending postcards where each card could only hold one bit of information (a simple "0" or "1"). This is like using a single-lane road; it works, but it's slow.

This paper describes a breakthrough where scientists managed to build a highway instead of a single-lane road. Here is how they did it, explained simply:

1. The Problem: The "Hybrid" Detour

Previous attempts to send more information at once (using "High-Dimensional" or HD-QKD) had to take a detour. Imagine you have a 4-lane highway (a special fiber optic cable with 4 separate paths inside it), but instead of using all 4 lanes at once, the old method used only 2 lanes and tried to squeeze extra information in by timing the cars (like sending a car at 1:00 PM vs. 1:01 PM).

This "hybrid" approach was clunky. It was like trying to drive a race car but having to stop at every intersection to check your watch. It wasted time and lost efficiency, especially when the road was bumpy or long.

2. The Solution: The "Full Core" Highway

The team at the University of Concepción in Chile decided to stop taking detours. They used a special 4-core fiber optic cable (a cable with 4 distinct "lanes" or cores inside one jacket).

Instead of mixing lanes and timing, they used all 4 lanes simultaneously to carry the message.

• The Analogy: Imagine you have 4 different colored flags. Instead of waving one flag at a time, you wave all four at once in a specific pattern. That single pattern carries much more information than just waving one flag.
• The Result: They successfully sent these complex "4-lane" messages across a real-world network connecting different university buildings (some 200 meters away, others 1.3 kilometers away).

3. The Challenge: The Bumpy Road

Sending these delicate quantum messages over a real city campus is hard. The cables run underground, under roads, and near people walking.

• The Noise: Trucks driving by, temperature changes, and people walking create vibrations. In quantum terms, this is like wind shaking your flags so hard you can't tell what pattern you're waving.
• The Fix: The scientists used a clever "stabilization" trick. They treated the 4 lanes like a choir. Even if the wind (vibrations) made the singers slightly out of tune, the fact that all 4 lanes were wrapped in the same protective jacket meant they drifted together. The scientists just had to make tiny, quick adjustments to keep the choir in harmony. They found that for 100 milliseconds (a blink of an eye), the signal stayed perfectly stable.

4. The Result: A New Speed Record

They tested their system with two types of "eyes" (detectors) to see how well it worked:

1. Standard Detectors: Like regular glasses. It worked, proving the system is viable with cheaper, commercial tech.
2. Super-Sensitive Detectors: Like high-tech night-vision goggles. With these, they achieved a record-breaking speed.

The Big Win:
At a signal loss of 10 dB (which is like the signal getting significantly weaker, similar to a long-distance call), they achieved a secret key rate of 0.00619 bits per pulse.

• Why this matters: This is nearly twice as fast as the previous best record for this type of high-speed quantum messaging.
• The Comparison: Before, the best high-speed quantum systems were about half as efficient as standard, simple quantum systems. This new method has closed that gap. They are now almost as fast as the best simple systems, but with the added benefit of carrying more data per photon.

Summary

Think of this paper as the team that finally figured out how to drive a 4-lane race car on a bumpy city street without crashing.

• Old way: Drive a slow car, stop often to check your watch (Hybrid encoding).
• New way: Drive a fast car using all 4 lanes at once, adjusting the steering wheel quickly to handle the bumps (Pure core-mode encoding).

They proved that you don't need a perfect, laboratory-only environment to do this. You can do it on a real university campus, and you can do it faster than ever before. This paves the way for secure, high-speed quantum internet that can actually be built in the real world.

Technical Summary

Technical Summary: High-Dimensional Quantum Key Distribution via Full Core-Mode Encoding over Deployed Multicore Fibers

Problem Statement
Quantum Key Distribution (QKD) offers information-theoretic security, but conventional qubit-based systems are limited by low noise tolerance and a maximum of one secret bit per detected photon. High-dimensional (HD) QKD, encoding information in $d$-dimensional Hilbert spaces ($d > 2$), addresses these limitations by increasing the error-rate threshold and potential secret-key yield. While multicore fibers (MCFs) are a natural substrate for HD-QKD due to their ability to support multiple path (core) modes, previous field demonstrations have relied on hybrid encoding strategies. These strategies combine a subset of core modes with an auxiliary degree of freedom, typically time-bin. Although robust, hybrid approaches incur intrinsic efficiency penalties: they reduce the qudit generation rate relative to the laser clock rate and require complex interferometric measurements (e.g., Franson-like interferometers) that discard a fraction of detected photons. Consequently, the theoretical advantages of HD-QKD have not been fully realized in practical, deployed networks.

Methodology
The authors implemented a four-dimensional ($d=4$) QKD protocol using pure core-mode encoding over a permanently installed MCF network at the Universidad de Concepción, Chile. Unlike previous hybrid approaches, this system utilizes the full set of four available cores in the fiber to encode logical states $|0\rangle, |1\rangle, |2\rangle, |3\rangle$, eliminating the need for time-bin multiplexing.

• System Architecture: The setup employs a prepare-and-measure scheme. Alice generates four-dimensional ququarts using a four-core multiport beam splitter (4C-MBS) and phase modulators (PMs) to control the relative phases of the core modes. The states are transmitted through the deployed MCF network to Bob, who performs measurements using a second 4C-MBS and single-photon detectors (SPDs).
• Network Environment: The experiment utilized three distinct link configurations: a back-to-back (BtB) reference, a 200 m link (P6) within a building, and a 1.3 km cross-campus link (PtE) traversing roads and pedestrian areas. These links were subject to continuous, uncontrolled environmental perturbations, including temperature variations and mechanical vibrations.
• Stabilization and Control: To maintain coherence across the cores, the system employs a phase-stabilization algorithm. Alice's PMs are biased to compensate for stochastic phase drifts accumulated during propagation, ensuring constructive interference at the target detector. The system operates in 100 ms acquisition windows, a duration determined to be sufficient for phase stability despite environmental noise.
• Detection and Analysis: The system was tested with two detector technologies: InGaAs avalanche photodiodes (commercially accessible, $\sim7.5\%$ efficiency) and superconducting nanowire single-photon detectors (SNSPDs, $\sim85\%$ efficiency). Secret key rates were estimated using a finite-key analysis based on the two-decoy-state method (Zhang et al.), which avoids Gaussian assumptions on statistical fluctuations to provide rigorous security bounds.

Key Contributions

1. First Field Deployment of Pure Core-Mode HD-QKD: This work represents the first demonstration of a $d=4$ HD-QKD system operating over a fully installed MCF network under real-world, uncontrolled conditions using only core modes for encoding.
2. Elimination of Hybrid Encoding Penalties: By utilizing all four cores directly, the system avoids the generation-rate penalties of time-bin schemes and the photon loss associated with time-bin projection interferometers.
3. Robustness in Real-World Environments: The study demonstrates that the common-cladding geometry of MCFs effectively suppresses differential phase drift, allowing for stable qudit propagation and high-fidelity state transmission (mean fidelity $\bar{F} = 0.96 \pm 0.01$) over a 1.3 km link despite significant environmental noise.
4. Finite-Key Benchmarking: The authors provide a composable finite-key rate analysis, establishing a new performance benchmark for HD-QKD at comparable channel losses.

Results

• Performance Metrics: At a channel attenuation of 10 dB, the system achieved a composable finite-key rate of $R = 6.19 \times 10^{-3}$ bits/pulse using SNSPDs.
• Comparative Advantage: This rate is nearly double the previous best reported for HD-QKD at comparable loss ($3.1 \times 10^{-3}$ bits/pulse for a time-bin implementation) and more than four times higher than a previous hybrid core+time-bin field demonstration.
• Detector Independence: Positive secret key rates were obtained with both InGaAs and SNSPD detectors, confirming the system's viability with commercially accessible hardware. The system demonstrated positive asymptotic key rates even at 20 dB of artificial attenuation.
• Stability: The QBER distribution remained stable over 100 ms windows, with the spread dominated by detector dark counts and timing jitter rather than phase drifts, validating the efficacy of the passive phase stabilization approach.

Significance
The paper claims that this result establishes core-mode encoding as a viable architecture for realistic, high-rate quantum-secure communications. By recovering the encoding efficiency lost in hybrid schemes, the intrinsic advantages of high-dimensional encoding (higher noise tolerance and information capacity) are no longer fully absorbed by system overhead. The achieved rate of $6.19 \times 10^{-3}$ bits/pulse brings HD-QKD within a factor of 1.5 of the current state-of-the-art qubit-based systems ($8.9 \times 10^{-3}$ bits/pulse), suggesting that HD-QKD has reached a regime of genuine practical competitiveness. Furthermore, the architecture is directly scalable to higher dimensions using MCFs with more cores, offering a pathway for future metropolitan quantum networks based on space-division multiplexing.