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Physical Review Applied

Optical frequency comb–based multichannel parallel continuous-variable quantum network coding

Tianai Zhou, Gang Xu, Yewei Guo, Tao Shang, Zongpeng Li, Xiu‐Bo Chen, Ying Guo

Published Jun 2, 2025• 3 citations
Publisher

Abstract

Quantum network coding provides a solution for information transmission at bottleneck channels. However, the single-path scheduling approach is hampered in the face of massive data transmission demands, which is particularly challenging in large-scale network communication scenarios. Here we propose a continuous-variable quantum network coding (CVQNC) scheme for parallel transmission of multiple quantum states based on optical frequency combs. The quantum communication channel is naturally constructed due to the nonclassical correlations exhibited by the symmetric sideband modes at around half the pump frequency on the squeezed field. Source nodes with preshared multiplex entanglement enable the transmission of multiple quantum states in parallel and simultaneously, which increases the channel capacity of the network and relieves the single-path transmission pressure. In particular, fidelity is calculated as a critical measure of transmission performance, and we provide a method to increase fidelity using photon catalysis, along with squeezing parameters and beam splitter transmittance for non-Gaussian source states at optimal fidelity. Furthermore, the channel capacity and fidelity of the CVQNC system are predicted on the basis of the $k$-nearest neighbor algorithm, and the predicted data match well with the actual derivation.

DOI
10.1103/physrevapplied.23.064003

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Quantum network coding provides a solution for information transmission at bottleneck channels. However, the single-path scheduling approach is hampered in the face of massive data transmission demands, which is particularly challenging in large-scale network communication scenarios. Here we propose a continuous-variable quantum network coding (CVQNC) scheme for parallel transmission of multiple quantum states based on optical frequency combs. The quantum communication channel is naturally constructed due to the nonclassical correlations exhibited by the symmetric sideband modes at around half the pump frequency on the squeezed field. Source nodes with preshared multiplex entanglement enable the transmission of multiple quantum states in parallel and simultaneously, which increases the channel capacity of the network and relieves the single-path transmission pressure. In particular, fidelity is calculated as a critical measure of transmission performance, and we provide a method to increase fidelity using photon catalysis, along with squeezing parameters and beam splitter transmittance for non-Gaussian source states at optimal fidelity. Furthermore, the channel capacity and fidelity of the CVQNC system are predicted on the basis of the kkk-nearest neighbor algorithm, and the predicted data match well with the actual derivation.
Channel multiplexing quantum communication based on exploiting continuous-variable entanglement of optical modes offers great potential to enhance channel capacity and save quantum resource. Here, we present a frequency-comb-type control scheme for simultaneously extracting a lot of entangled sideband modes with arbitrary frequency detuning from a squeezed state of light. We experimentally demonstrate fourfold channel multiplexing quantum dense coding communication by exploiting the extracted four pairs of entangled sideband modes. Due to high entanglement and wide frequency separation between each entangled pairs, these quantum channels have large channel capacity and the cross talking effect can be avoided. The achieved channel capacities have surpassed that of all classical and quantum communication under the same bandwidth published so far. The presented scheme can be extended to more channels if more entangled sideband modes are extracted.
ABSTRACT Continuous‐variable quantum network coding (CVQNC) faces several challenges when extended to large scale scenarios, including the insufficient channel capacity, low entanglement generation efficiency, and degradation of entanglement under channel loss. In this study, a high‐capacity CVQNC scheme based on microcavity frequency combs is proposed over the butterfly network, which enables parallel quantum information transmission among multiple user pairs by exploiting network coding at the bottleneck link. Furthermore, an entanglement enhancement strategy combining mode multiplexing with quantum scissors is introduced to reduce the entanglement degradation caused by channel loss. The results show that the proposed scheme improves the entanglement enhancement efficiency, channel capacity, transmission fidelity, and security while scaling to a larger number of users.
In classical communication, the introduction of polychromatic resources has rapidly boosted classical networks' rate and scale. Quantum communication is now at a similar critical stage in its development, and therefore, it is essential to investigate polychromatic quantum communication networks. In this letter, we report a polychromatic continuous-variable quantum communication network enabled by optical frequency combs. The multi-mode density matrices constituted by polychromatic quantum networks are studied. Considering the limited mode isolation, the maximum amount of information that eavesdroppers can obtain is recalculated, therefore, the total secret key rate is provided. We have also demonstrated that, compared to other multiplexing techniques, polychromatic quantum networks can theoretically achieve a secret key rate without decreasing with the increase in users. In the experiment, direct-transmission type and round-trip type quantum communication networks were built using optical frequency combs and dual-comb interference detection technology. The Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) protocol has been validated, with a network capacity of 19 and a total secret key rate of 8.75 Gbps at a uniform distance of 5 km (asymptotic case), 0.82 Mbps at 120 km (finite-size effect), 89.10 Mbps at 40 km (compsable security), 13.66 Mbps at 40 km (compsable finite-size security). This implementation not only provides technical support for a high-speed multi-node quantum network, but also provides a solution for the future quantum Internet with continuous variables.
Continuous-variable quantum key distribution (CVQKD) provides an approach for secure communication in optical fiber communication systems. However, its practical implementation has been hindered by low secret key bit rates that are usually limited to several bits/s to hundreds of kbits/s at distances of more than 25 kilometers. In this paper, we use a pair of optical frequency combs (OFCs) for both multiple parallel transmission and coherent reception, which assign multiple sub-channels involving multiple independent secret keys in a single fiber to increase the key bit rate. The first and last sub-channels are selected for propagating phase references to compensate the phase offset between two free-running combs. We analyze possible excess noise caused by dispersive walk-off in the transmission, imperfect phase compensation in the reception and photon leakage from the phase references. Compared to the previous single-channel CVQKD method, simulation results show more than a factor of 20 increase in the secret key rate at a transmission distance of 35 km and the number of comb lines of 35.
Quantum key distribution with continuous variables already uses advantageous high-speed single-mode homodyne detection with low electronic noise at room temperature. Together with continuous-variable information encoding to nonclassical states, the distance for secure key transmission through lossy channels can approach 300 km in current optical fibers. Such protocols tolerate higher channel noise and also limited data processing efficiency compared to coherent-state protocols. The secret key rate can be further increased by increasing the system clock rates, and, further, by a suitable frequency-mode-multiplexing of optical transmission channels. However, the multiplexed modes couple together in the source or any other part of the protocol. Therefore, multiplexed communication will experience cross talk and the gain can be minuscule. Advantageously, homodyne detectors allow solving this cross-talk problem by proper data processing. It is a potential advantage over protocols with single-photon detectors, which do not enable similar data processing techniques. We demonstrate the positive outcome of this methodology on the experimentally characterized frequency-multiplexed entangled source of femtosecond optical pulses with natural cross talk between eight entangled pairs of modes. As the main result, we predict the almost 15-fold higher secret key rate. This experimental test and analysis of frequency-multiplexed entanglement source open the way for the field implementation of high-capacity quantum key distribution with continuous variables.
Quantum secret sharing (QSS) faces inherent limitations in scaling to multi-user networks due to excess noise introduced by highly asymmetric beam splitters (HABSs) in chain-structured topologies. To overcome this challenge, we propose an optical frequency comb-based continuous-variable QSS (OFC CV-QSS) scheme that establishes parallel frequency channels between users and the dealer via OFC-generated multi-wavelength carriers. By replacing the chain-structured links with dedicated frequency channels and integrating the Chinese remainder theorem (CRT) with a decentralized architecture, our design eliminates excess noise from all users using HABS while providing mathematical- and physical-layer security. Simulation results demonstrate that the scheme achieves a more than 50% improvement in maximum transmission distance compared to chain-based QSS, with significantly slower performance degradation as users scale to 20. Numerical simulations confirm the feasibility of this theoretical framework for multi-user quantum networks, offering dual-layer confidentiality without compromising key rates.