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Quantum Computing, Communication, and Simulation

High-dimensional Quantum Networks: deploying the frequency and time modalities

Kemal Enes Akyuz, Kai-Chi Chang, Murat Can Sarihan, Yujie Chen, Cody Fan, Xiang Cheng, Christina Huang, Chee Wei Wong

Published Mar 5, 2026• 0 citations
Publisher

Abstract

Quantum networks enable fundamentally secure communications and entanglement distribution in parallelized quantum computation. Here we describe our high-dimensional quantum network based on frequency-multiplexed time-bin encoding. Our multi-user 21-km experimental testbed is designed for robustness and scalability, with frequency- and temporal-multiplexing for high-rate interconnects while preserving minimal resource usage and multi-party access through simultaneous key or entanglement distribution. Our measurements are in the high-dimensional frequency and temporal conjugate subspaces, via our biphoton frequency comb qudit. Non-local Franson interferometry provide a measured lower-bound of our entanglement-of-formation, and the Schmidt mode decomposition provide an estimate of the accessible quantum information. We highlight adaptive optimization and singly-filtered biphoton combs as a practical architecture in our high-rate quantum network testbed. We describe the photon information efficiency, Shannon capacity, entanglement distribution, raw key rates, security measurements, dispersive bases, code-efficient non-binary error correction, and Holevo bounds embedded in our network.

DOI
10.1117/12.3092130

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Quantum networks enable fundamentally secure communications and entanglement distribution in parallelized quantum computation. Here we describe our high-dimensional quantum network based on frequency-multiplexed time-bin encoding. Our multi-user 21-km experimental testbed is designed for robustness and scalability, with frequency- and temporal-multiplexing for high-rate interconnects while preserving minimal resource usage and multi-party access through simultaneous key or entanglement distribution. Our measurements are in the high-dimensional frequency and temporal conjugate subspaces, via our biphoton frequency comb qudit. Non-local Franson interferometry provide a measured lower-bound of our entanglement-of-formation, and the Schmidt mode decomposition provide an estimate of the accessible quantum information. We highlight adaptive optimization and singly-filtered biphoton combs as a practical architecture in our high-rate quantum network testbed. We describe the photon information efficiency, Shannon capacity, entanglement distribution, raw key rates, security measurements, dispersive bases, code-efficient non-binary error correction, and Holevo bounds embedded in our network.
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.
Abstract High-dimensional quantum entanglement is a cornerstone for advanced technology enabling large-scale noise-tolerant quantum systems, fault-tolerant quantum computing, and distributed quantum networks. The recently developed biphoton frequency comb (BFC) provides a powerful platform for high-dimensional quantum information processing in its spectral and temporal quantum modes. Here we propose and generate a singly-filtered high-dimensional BFC via spontaneous parametric down-conversion by spectrally shaping only the signal photons with a Fabry-Pérot cavity. High-dimensional energy-time entanglement is verified through Franson-interference recurrences and temporal correlation with low-jitter detectors. Frequency- and temporal- entanglement of our singly-filtered BFC is then quantified by Schmidt mode decomposition. Subsequently, we distribute the high-dimensional singly-filtered BFC state over a 10 km fiber link with a post-distribution time-bin dimension lower bounded to be at least 168. Our demonstrations of high-dimensional entanglement and entanglement distribution show the singly-filtered quantum frequency comb’s capability for high-efficiency quantum information processing and high-capacity quantum networks.
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.
Quantum entanglement is a fundamental resource for secure information processing and communications. The canonical optical quantum information processing encodes a single qubit per photon, with remarkable demonstrations of secure quantum communications, linear optical quantum computing amongst others. Often the polarization qubit, a discrete variable with entangled Bell states, is used. Continuous variables such as energy-time modes and spatial modes, however, present a dramatically larger Hilbert space for quantum information processing. The high-dimensional entanglement capture more qubits per photon, enabling dramatically higher secure key rates over longer distances and with better error resilience. Here I will describe our results on high-dimensional entanglement in quantum frequency combs for dense quantum communications. We first demonstrate revival of the Hong-Ou-Mandel interferences, long postulated by theorists more than a decade ago, up to 19-dimensions and with visibilities up to 96.5%. The mode-locked two-photon state in high-dimensions is further witnessed through a stabilized Franson interferometer, as a generalized Bell’s inequality test and hyperentangled through multiple degrees-of-freedom. Entanglement revivals of the non-local interference at discrete time-bins are uncovered, up to 97.8% visibility, as a fundamental resource for dense secure information processing.
High-dimensional photonic entanglement holds significant promise for advancing quantum communication, computation, and metrology. For example, large-alphabet quantum communication protocols are known to benefit from enhanced noise resilience and information capacity via multi-bit time-bin encoding. Yet, characterizing high-dimensional entangled states is challenging, as full state tomography becomes prohibitively costly and often requires unrealizable measurements. Here, we demonstrate a scan-free method to characterize high-dimensional entanglement in the time-frequency domain. Our reconstruction achieves a record 5.70±0.075.70\pm0.075.70±0.07 ebits and a fidelity of 65.4±0.4%65.4\pm0.4\%65.4±0.4% with the maximally entangled state of local dimension 102110211021, certifying the presence of 668668668-dimensional entanglement. We further prove the attainability of a secure key rate of 15.615.615.6 kB/s in a composable finite-size, entanglement-based protocol, and show that in continuous operation, the setup can quickly approach asymptotic key rates. Using commercial telecom components and state-of-the-art low-jitter single-photon detectors, our scalable architecture offers a practical path towards high-rate, noise-resilient quantum communication testbeds.