Lukas Scarfe, Yingwen Zhang, and Ebrahim Karimi at the University of Ottawa and the National Research Council of Canada have demonstrated a quantum key distribution protocol achieving a maximum sifted key rate of 0.9 Kb/s with 361 modes. The work utilizes the relationship between position and momentum to remotely prepare photons in specific spatial modes, encoding information with an efficiency of 5.07 bits per photon using 90 spatial modes. Researchers theoretically show this spatial-mode encoding could reach over 700 Mb/s at 4400 modes with improved technology, quantifying the potential of high-dimensional quantum communication systems.

Spatial Mode Encoding Unlocks High-Dimensional QKD

The protocol utilizes entangled photon pairs generated through spontaneous parametric down-conversion, where one photon’s measurement dictates the state of its partner, enabling secure key exchange. This approach differs from traditional QKD methods which often rely on fewer modes and more intricate state preparation. The experiment centered on exploiting the mutually unbiased nature of position and momentum, linked mathematically by a Fourier transform, to encode quantum information.

Alice, the sender, directs photons through a beam splitter that randomly assigns them to either a position or momentum basis for measurement. This projective measurement remotely prepares the corresponding spatial mode in Bob’s, the receiver’s, photon, which is then measured using an identically configured setup.

Event-based single-photon cameras were used, allowing for high-resolution coincidence imaging in both position and momentum bases, and access to a greater number of spatial modes. The current demonstration is limited by the quantum efficiency, spatial, and timing resolution of the single-photon cameras and the brightness of the entangled photon source, but theoretical modeling suggests significant scalability. The researchers predict that employing brighter entangled photon sources alongside next-generation superconducting nanowire array cameras could push photon efficiencies to 9 bits per photon at 2000 spatial modes.

They project secret-key rates exceeding 700 Mb/s at 4400 modes, accounting for finite-key effects, practical considerations that arise when dealing with a limited number of key exchanges. These projections quantify the potential of spatially encoded, entanglement-based QKD and establish a benchmark for future developments in high-dimensional quantum communication.

The inherent randomness of the spatial mode, stemming from the position-momentum entanglement, eliminates the need for external random number generators. Similarly, the selection of the measurement basis, position or momentum, is determined passively by the beam splitter, simplifying the experimental setup and reducing potential vulnerabilities.

5.07 Bits/Photon Achieved with 90 Spatial Modes

This result, detailed in a new study, offers a pathway to significantly increased key rates. The experiment leverages the inherent link between a photon’s position and momentum, utilizing these conjugate variables as mutually unbiased bases for encoding quantum information. This approach allows for remote preparation of photons in specific spatial modes. The core of the protocol centers on entanglement; pairs of photons are generated with correlated position and momentum. This measurement, performed passively, remotely prepares the partner photon in a corresponding spatial mode, which is then transmitted to a receiver employing an identical setup.

Scalability Modeling: Projecting 9 Bits/Photon at 2000 Modes

This rate, while modest, represents an advancement in high-dimensional quantum key distribution (QKD) because it was previously difficult to attain with schemes employing numerous spatial modes. The core of their system relies on generating entangled photon pairs via spontaneous parametric down-conversion, then passively directing one photon through a beam splitter to randomly select between measuring its position or momentum. This efficiency metric quantifies how much quantum information is reliably encoded per detected photon, a key parameter for practical QKD systems.

Specifically, the modeling suggests that 9 bits per photon could be achieved at 2000 spatial modes, a significant leap from the current 5.07 bits per photon achieved using 90 spatial modes. The theoretical calculations project a bit rate exceeding 700 Mb/s at 4400 modes, a speed that would bring QKD closer to practical application in high-bandwidth communication networks.

These projections account for finite-key effects, a critical consideration for real-world security analysis. The anticipated performance boost hinges on advancements in single-photon camera technology. Next-generation superconducting nanowire array cameras, with their improved specifications, are expected to overcome these limitations, enabling the detection of a greater number of spatial modes with higher fidelity. This simplification reduces the potential for side-channel attacks and streamlines the implementation of the protocol.

The team’s work demonstrates a clear pathway towards scaling up the number of spatial modes used in QKD, potentially unlocking significantly higher key rates and improved security for quantum communication networks. The modeling provides a valuable roadmap for hardware development, highlighting the critical role of brighter entangled photon sources and high-performance single-photon detectors in realizing the full potential of this promising technology.

SPDC Source & Single-Photon Camera Implementation

High-dimensional quantum key distribution (QKD) achieved a maximum sifted key rate of 0.9 kilobits per second in a recent demonstration, marking a step toward practical quantum communication systems. The experimental setup centers around spontaneous parametric down-conversion (SPDC), a process where entangled photon pairs are generated, and a novel implementation of measurement.

This passive selection of measurement basis eliminates the need for complex optical modulation or external random number generators, streamlining the process and reducing potential security vulnerabilities. The experiment involved measuring correlations in both the horizontal and vertical directions, revealing near-identical results and confirming the effectiveness of the spatial encoding scheme.

700 Mb/s Key Rates Projected with Advanced Detectors

This experiment, detailed in a new paper, uses 90 spatial modes to achieve a photon information efficiency of 5.07 bits per photon, and 0.9 Kb/s with 361 modes, significantly increasing the potential information capacity per photon. Detecting these photons required event-based single-photon cameras capable of precisely timing and spatially resolving individual photon arrivals, allowing for high-resolution coincidence imaging.

This projection accounts for the practical limitations imposed by finite-key effects, which arise from the finite amount of data used in key generation. The choice of position and momentum as mutually unbiased bases offers a unique advantage in simplifying the implementation of the QKD protocol. Unlike some high-dimensional schemes that require complex optical modulation, this method relies on the intrinsic properties of the entangled photon pairs and passive beam splitters for state preparation and basis selection.

This simplification reduces the complexity of the system and potentially lowers the cost of deployment. The researchers emphasize that this initial demonstration focused on characterizing the high-dimensional encoding itself, establishing a valuable benchmark for future quantum communication systems. This work provides a quantifiable assessment of the opportunities and performance bounds of spatially encoded, entanglement-based QKD.

By demonstrating the feasibility of encoding information in a large number of spatial modes and projecting significant performance gains with improved hardware, the study offers a clear roadmap for advancing high-dimensional quantum communication. The results serve as a crucial reference point for evaluating and comparing future QKD systems. The team’s findings establish a foundation for future research aimed at realizing the full potential of high-dimensional quantum key distribution and its role in securing communication in an increasingly interconnected world.

👉 More information
🗞 Spatial mode encoding for quantum key distribution: From hundreds to thousands of modes
✍️ Lukas Scarfe, Yingwen Zhang and Ebrahim Karimi
🧠 DOI: http://link.aps.org/doi/10.1103/x9qt-4qt3

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