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npj Quantum Information

Realizing ultrahigh capacity quantum superdense coding on quantum photonic chip

Yuan Li, Huihui Zhu, Wei Luo, Hong Nian Cai, Muhammad Faeyz Karim, Xianshu Luo, Feng Gao, Xiang Xia Wu, Xiaoqi Zhou, Qinghua Song, L. C. Kwek, A. Q. Liu

Published Mar 18, 2025• 9 citations
Publisher

Abstract

Quantum superdense coding provides a compelling solution to enhance the channel capacity compared with classical coding, which plays a vital role in quantum networks. However, the realization of a degenerate high-dimensional entangled state with high fidelity has remained an elusive challenge, limiting improvement in channel capacity. Here, we have demonstrated a 16-mode quantum process photonic chip and experimentally validated a degenerate eight-dimensional quDit entangled state with a fidelity of $${{0.973}}\pm {{0.002}}$$ . Moreover, we propose an efficient Bell state measurement method to distinguish eleven orthogonal Bell states in eight-dimensional quantum superdense coding. Leveraging the high-quality features of our quantum photonic chip, we have achieved an unprecedented channel capacity of $${{3.021}}\pm {{0.003}}$$ bits, highlighting the largest channel capacity to date. Furthermore, our method presents a remarkable quantum advantage over classical schemes, the latter of which can only transmit a maximum of 3 bits in the environment without any noise. Our findings not only open up a new avenue for integrated quantum information processing, but also contribute significantly to the advancement of multidimensional technologies, facilitating the establishment of practical, high-capacity quantum networks.

DOI
10.1038/s41534-025-01007-y

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Quantum superdense coding provides a compelling solution to enhance the channel capacity compared with classical coding, which plays a vital role in quantum networks. However, the realization of a degenerate high-dimensional entangled state with high fidelity has remained an elusive challenge, limiting improvement in channel capacity. Here, we have demonstrated a 16-mode quantum process photonic chip and experimentally validated a degenerate eight-dimensional quDit entangled state with a fidelity of 0.973±0.002{{0.973}}\pm {{0.002}}0.973±0.002 . Moreover, we propose an efficient Bell state measurement method to distinguish eleven orthogonal Bell states in eight-dimensional quantum superdense coding. Leveraging the high-quality features of our quantum photonic chip, we have achieved an unprecedented channel capacity of 3.021±0.003{{3.021}}\pm {{0.003}}3.021±0.003 bits, highlighting the largest channel capacity to date. Furthermore, our method presents a remarkable quantum advantage over classical schemes, the latter of which can only transmit a maximum of 3 bits in the environment without any noise. Our findings not only open up a new avenue for integrated quantum information processing, but also contribute significantly to the advancement of multidimensional technologies, facilitating the establishment of practical, high-capacity quantum networks.
Quantum superdense coding protocols enhance channel capacity by using shared quantum entanglement between two users. The channel capacity can be as high as 2 when one uses entangled qubits. However, this limit can be surpassed by using high-dimensional entanglement. We report an experiment that exceeds the limit using high-quality entangled ququarts with fidelities up to 0.98, demonstrating a channel capacity of 2.09 ± 0.01. The measured channel capacity is also higher than that obtained when transmitting only one ququart. We use the setup to transmit a five-color image with a fidelity of 0.952. Our experiment shows the great advantage of high-dimensional entanglement and will stimulate research on high-dimensional quantum information processes.
Quantum protocols require access to large-scale entangled quantum states, due to the requirement of channel capacity. As a promising candidate, the high-dimensional orbital angular momentum (OAM) entangled states have been implemented, but only one of four OAM Bell states in each individual subspace can be distinguished. Here we demonstrate the first realization of complete OAM Bell-state measurement (OAM-BSM) in an individual subspace, by seeking the suitable unitary matrix performable using only linear optics and breaking the degeneracy of four OAM Bell states in ancillary polarization dimension. We further realize the superdense coding via our complete OAMBSM with the average success probability of ~82% and the channel capacity of ~1.1(4) bits. This work opens the window for increasing the channel capacity and extending the applications of OAM quantum states in quantum information in future.
Quantum networks provide a versatile infrastructure for communication, computing, and sensing with quantum information. Novel sources and detectors for transmitting and receiving quantum states are critical elements in the development and eventual deployment of robust quantum networks. Alongside performance, the compatibility of quantum network devices with modern networking infrastructure is an important requirement for deployment. We present results on the integration of quantum communication using superdense coding transmitted over optical fiber links into network environments. Our approach takes advantage of a novel complete Bell-state measurement setup that relies on hyper-entanglement in the temporal and polarization degrees of freedom for a two-photon state emitted from a quantum light source. Using linear optics and common single-photon detectors, we record a single-qubit channel capacity of 1.665±0.018. We then demonstrate a full experimental implementation of hybrid, quantum-classical communication protocol for image transfer applications. Our devices integrate with existing fiber optical network and software-defined transmitters and receivers as part of a modular design to provide an extensible quantum communication system that can adapt to future quantum technology goals.
Quantum networks provide a versatile infrastructure for communication, computing, and sensing with quantum information. Novel sources and detectors for transmitting and receiving quantum states are critical elements in the development and eventual deployment of robust quantum networks. Alongside performance, the compatibility of quantum network devices with modern networking infrastructure is an important requirement for deployment. We present results on the integration of quantum communication using superdense coding transmitted over optical fiber links into network environments. Our approach takes advantage of a novel complete Bell-state measurement setup that relies on hyper-entanglement in the temporal and polarization degrees of freedom for a two-photon state emitted from a quantum light source. Using linear optics and common single-photon detectors, we record a single-qubit channel capacity of 1.665±0.018. We then demonstrate a full experimental implementation of hybrid, quantum-classical communication protocol for image transfer applications. Our devices integrate with existing fiber optical network and software-defined transmitters and receivers as part of a modular design to provide an extensible quantum communication system that can adapt to future quantum technology goals.
A method of generating superdense coding based on quantum hyper-entanglement and facilitated by quantum networks is discussed. Superdense coding refers to the coding of more than one classical bit into each qubit. Quantum hyperentanglement refers to quantum entanglement in more than one degree of freedom, e.g. polarization, energy-time, and orbital angular momentum (OAM). The new superdense coding scheme permits 2L bits to be encoded into each qubit where L is the number of degrees of freedom used for quantum hyper-entanglement. The superdense coding procedure is based on a generalization of the Bell state for L degrees of freedom. Theory describing the structure, generation/transmission, and detection of the generalized Bell state is developed. Circuit models are provided describing the generation/transmission process and detection process. Detection processes are represented mathematically as projection operators. A mathematical proof that that the detection scheme permits the generalized Bell states to be distinguished with 100% probability is provided. Measures of effectiveness (MOEs) are derived for the superdense coding scheme based on open systems theory represented in terms of density operators. Noise and loss related to generation/transmission, detection and propagation are included. The MOEs include various probabilities, quantum Chernoff bound, a measure of the number of message photons that must be transmitted to successfully send and receive a message, SNR and the quantum Cramer Rao’ lower bound. Quantum networks with quantum memory are used to increase the efficiency of the superdense coding scheme.
With the assistance of auxiliary two-dimensional polarization entanglement, we theoretically present an efficient Bell state measurement (BSM) method for photonic four-dimensional entanglement in the path degree of freedom, in which just simple linear optical elements and common single-photon detectors are utilized. With this approach, the 16 mutually orthogonal four-dimensional path Bell states can be classified into eight distinguishable groups, which allows the transmission of 3 bits of classical information by just sending one photon in our quantum superdense coding protocol. Compared with previous quantum dense coding protocols that are also based on linear-optical BSM, our protocol has certain advantages and will be useful for other quantum communication protocols based on high-dimensional entanglement.