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Towards high-dimensional frequency-bin quantum key distribution in a multi-user quantum network

Meritxell Cabrejo Ponce, Fabian Steinlechner

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

We develop methods to harness the high-dimensional entanglement of biphoton quantum frequency combs for frequency-multiplexed, multi-user networks. Using matrix completion techniques and computing asymptotic keys, we investigate the impact of dimension-dependent noise and identify the optimal dimension for encoding quantum information.

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Abstract Quantum networks enhance quantum communication schemes and link multiple users over large areas. Harnessing high dimensional quantum states - qu-d-its - allows for a denser transfer of information with increased robustness to noise compared to qubits. Frequency encoded qu-d-its can be manipulated at telecom wavelengths with off-the-shelf fibered devices. We use a low free spectral range silicon microresonator to propose, assess and optimize a reconfigurable entanglement-based quantum key distribution network with frequency-bin encoded Bell states of dimension d = 2 and d = 3, using a single fibered hardware. We achieve secure key rates of 1374 bit/s with qutrits ( d = 3), and estimate the communication range to 295 km with qubits ( d = 2) across 21 parallel two-user quantum channels. This multi-dimensional versatile demonstration is stable beyond 21 h and lays the groundwork for larger dimensionality implementations deployed on metropolitan fiber links.
High-dimensional entanglement with larger Hilbert spaces enable an encoding of more bits per photon and thus promise increased communication capacities over quantum channels. Quantum frequency combs, which are intrinsically multimode in the temporal and frequency degrees of freedom within a single spatial mode, naturally facilitating the generation and measurement of high-dimensional entanglement. Current challenges include the extension of well-known methods for two qubits to high-dimensional quantum systems and their application in entanglement experiments with photons. More specifically, the major challenge is the certification of high-dimensional entanglement by a number of accessible experimental measurements. In this paper, we increase the Hilbert space dimensionality and provide versatile tools for quantifying and certifying high-dimensional entanglement in a biphoton frequency comb. We quantify the time binned Schmidt number up to 18 and certify entanglement of formation with 1.89 ebits. We have demonstrated a 648- dimensional Hilbert spaces with time-frequency entanglement in a biphoton frequency comb, enabling a computational space up to 13 photonic qubits, and 6.28 bits/photon classical information capacity. This high-dimensional time frequency multimode quantum states of biphoton frequency comb significantly boosting the photon information capacity that is critical for large-scale quantum information processing. Biphoton frequency comb has indeed demonstrated an attractive and powerful approach towards achieving this fundamental goal with applications in high-dimensional quantum information processing, time-frequency cluster-state quantum computation, high-dimensional encoding in quantum networks, and high-dimensional quantum simulations.