Quantum key distribution (QKD) has established itself as a groundbreaking technology, showcasing inherent security features that are fundamentally proven. Qubit-based QKD protocols that rely on binary encoding encounter an inherent constraint related to the secret key capacity. This limitation restricts the maximum secret key capacity to one bit per photon. On the other hand, qudit-based QKD protocols have their advantages in scenarios where photons are scarce and noise is present, as they enable the transmission of more than one secret bit per photon. While proof-of-principle entangled-based qudit QKD systems have been successfully demonstrated over the years, the current limitation lies in the maximum distribution distance, which remains at 20 km fiber distance. Moreover, in these entangled high-dimensional QKD systems, the witness and distribution of quantum steering have not been shown before. Here we present a high-dimensional time-bin QKD protocol based on energy-time entanglement that generates a secure finite-length key capacity of 2.39 bit/coincidences and secure cryptographic finite-length keys at 0.24 Mbits s⁻¹ in a 50 km optical fiber link. Our system is built entirely using readily available commercial off-the-shelf components, and secured by nonlocal dispersion cancellation technique against collective Gaussian attacks. Furthermore, we set new records for witnessing both energy-time entanglement and quantum steering over different fiber distances. When operating with a quantum channel loss of 39 dB, our system retains its inherent characteristic of utilizing large-alphabet. This enables us to achieve a secure key rate of 0.30 kbits s⁻¹ and a secure key capacity of 1.10 bit/coincidences, considering finite-key effects. Our experimental results closely match the theoretical upper bound limit of secure cryptographic keys in high-dimensional time-bin QKD protocols (Mower et al 2013 Phys. Rev. A 87 062322; Zhang et al 2014 Phys. Rev. Lett. 112 120506), and outperform recent state-of-the-art qubit-based QKD protocols in terms of secure key throughput using commercial single-photon detectors (Wengerowsky et al 2019 Proc. Natl Acad. Sci. 116 6684; Wengerowsky et al 2020 npj Quantum Inf. 6 5; Zhang et al 2014 Phys. Rev. Lett. 112 120506; Zhang et al 2019 Nat. Photon. 13 839; Liu et al 2019 Phys. Rev. Lett. 122 160501; Zhang et al 2020 Phys. Rev. Lett. 125 010502; Wei et al 2020 Phys. Rev. X 10 031030). The simple and robust entanglement-based high-dimensional time-bin protocol presented here provides potential for practical long-distance quantum steering and QKD with multiple secure bits-per-coincidence, and higher secure cryptographic keys compared to mature qubit-based QKD protocols.

中文翻译：

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大字母表时间仓量子密钥分配和通过色散光学的爱因斯坦-波多尔斯基-罗森转向


量子密钥分发 (QKD) 已成为一项突破性技术，展示了经过根本验证的固有安全功能。依赖于二进制编码的基于量子位的 QKD 协议遇到了与密钥容量相关的固有约束。此限制将最大秘密密钥容量限制为每个光子一位。另一方面，基于 qdit 的 QKD 协议在光子稀缺且存在噪声的情况下具有其优势，因为它们能够为每个光子传输多个秘密位。虽然基于纠缠的原理验证 qdit QKD 系统多年来已成功演示，但目前的限制在于最大分发距离，仍为 20 公里光纤距离。而且，在这些纠缠的高维QKD系统中，量子转向的见证和分布以前从未被展示过。在这里，我们提出了一种基于能量时间纠缠的高维时间仓 QKD 协议，该协议生成 2.39 位/巧合的安全有限长度密钥容量和 0.24 Mbits s ⁻¹ 的安全加密有限长度密钥在50公里的光纤链路中。我们的系统完全使用现成的商业现成组件构建，并通过非局部色散消除技术来抵御集体高斯攻击。此外，我们还创下了不同光纤距离上的能量时间纠缠和量子转向的新记录。当量子信道损耗为 39 dB 时，我们的系统保留了利用大字母表的固有特性。考虑到有限密钥效应，这使我们能够实现 0.30 kbits s ⁻¹ 的安全密钥速率和 1.10 位/巧合的安全密钥容量。 我们的实验结果与高维时间仓 QKD 协议中安全密钥的理论上限非常吻合（Mower 等人 2013 Phys. Rev. A 87 062322；Zhang 等人 2014 Phys. Rev. Lett. 112 120506），并且在使用商用单光子探测器的安全密钥吞吐量方面优于最新的基于量子位的 QKD 协议（Wengerowsky 等人 2019 Proc. Natl Acad. Sci. 116 6684；Wengerowsky 等人 2020 npj Quantum Inf. 6 5；Zhang 等人 2014 Phys. Rev. Lett. 112 120506；Zhang 等人 2019 Nat. Photon. 13 839；Liu 等人 2019 Phys. Rev. Lett. 122 160501；Zhang 等人 2020 Phys. Rev. Lett. 122 160501 125 010502；Wei 等人 2020 Phys. Rev. X 10 031030）。这里提出的简单而强大的基于纠缠的高维时间仓协议为实用的长距离量子引导和 QKD 提供了潜力，具有多个安全位每次重合，以及与成熟的基于量子位的 QKD 协议相比更高的安全加密密钥。