High-dimensional quantum key distribution with Qubit-like states

Click here for the full manuscript published in Communications Physics

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While Quantum Key Distribution (QKD) is theoretically secure, moving from theory to the real world is difficult. My recent research focuses on bridging the gap between high-dimensional protocols—which can carry more information per photon—and the technical simplicity required for practical, commercial hardware. We achieve this by using “qubit-like” states in a high-dimensional space, which we call Fourier-qubits (F-qubits).

The Problem: The Complexity of High Dimensions

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Most QKD systems today operate in two dimensions (using qubits), like the polarization of light. High-dimensional (HD) QKD is attractive because it allows us to send more than one bit of information per photon and provides better tolerance against noise and eavesdropping.

However, the “go-to” high-dimensional protocols require states that are superpositions of all possible values in a given dimension $d$. As $d$ increases, the experimental setup becomes exponentially more complex and prone to errors. This technical hurdle is the primary reason most commercial systems still stick to simple two-dimensional protocols.

Our Solution: Fourier-Qubits

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We introduced a protocol that uses the standard logical basis (the computational basis) but replaces the complex Fourier basis with F-qubits.

An F-qubit is a superposition of only two logical states, regardless of how high the dimension of the system is. The information is stored in the relative phase between these two states, which can take $d$ different values.

Why this works:

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• Simpler Hardware: Because we only ever interfere two states at a time, the measurement complexity remains constant even as the dimension grows.
• High Efficiency: In systems using Spatial Light Modulators (SLMs), F-qubits utilize the active area of the device much more efficiently than traditional high-dimensional states.
• Security: We mathematically proved that even though these states look “two-dimensional,” they can still be used to bound the information leaked to an eavesdropper in a high-dimensional Hilbert space.

Experimental Demonstration

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To test the protocol, we built a lab-scale free-space link using the Orbital Angular Momentum (OAM) of light. We used a 4-dimensional Hilbert space where information is encoded in the “twist” of the light beam.

The Setup:

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• Source: A 633 nm laser and a Spatial Light Modulator (SLM) to shape the F-qubit modes.
• The Channel: We simulated real-world atmospheric conditions using a turbulent cell and used an adaptive optics system (a deformable mirror) to correct the wavefront in real-time.
• The Result: Even with added noise, we achieved a secret key rate of 1.28 bits per photon. This is significantly higher than the theoretical limit of 1 bit per photon for standard two-dimensional systems.

Key Takeaways

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Our work demonstrates that you don’t need infinitely complex quantum states to reap the rewards of high-dimensional communication.

1. Efficiency: We maintained the benefit of increased information density ($\log_2(d)$ bits per photon).
2. Robustness: The protocol remained secure and functional in a noisy, turbulent environment.
3. Scalability: By fixing the measurement complexity to two modes, we’ve created a path for high-dimensional QKD that is actually feasible for next-generation telecommunications.

Conclusion

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The introduction of F-qubits offers a practical “middle ground” for quantum communications. It provides the high-speed performance of high-dimensional spaces without the traditional experimental headaches. We foresee this being particularly useful in bandwidth-limited channels, such as satellite-to-ground links or fiber networks where detector recovery times usually limit speed.