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QuESat: Satellite-Assisted Quantum Internet for Global-Scale Entanglement Distribution

Abstract

Entanglement distribution across remote distances is critical for many quantum applications. Currently, the de facto approach for remote entanglement distribution relies on optical fiber for on-the-ground entanglement distribution. However, the fiber-based approach is incapable of global-scale entanglement distribution due to intrinsic limitations. This paper investigates a new hybrid ground-satellite quantum network architecture (QuESat) for global-scale entanglement distribution, integrating an on-the-ground fiber network with a global-scale passive optical network built with low-Earth-orbit satellites. The satellite network provides dynamic construction of photon lightpaths based on near-vacuum beam guides constructed via adjustable arrays of lenses, forwarding photons from one ground station to another with very high efficiency over long distances compared to using fiber. To assess the feasibility and effectiveness of QuESat for global communication, we formulate lightpath provisioning and entanglement distribution problems, considering the orbital dynamics of satellites and the time-varying entanglement demands from ground users. A two-stage algorithm is developed to dynamically configure the beam guides and distribute entanglements, respectively. The algorithm combines randomized and deterministic rounding for lightpath provisioning to enable global connectivity, with optimal entanglement swapping for distributing entanglements to meet users’ demands. By developing a groundsatellite quantum network simulator, QuESat achieves multi-fold improvements compared to repeater networks.

Index Terms—Entanglement distribution, passive optical quantum network, ground-satellite hybrid architecture, lightpath provisioning, entanglement traffic engineering

跨越长距离的纠缠分发对于众多量子应用至关重要。当前，远程纠缠分发的事实标准方法依赖于地面光纤网络。然而，由于其固有的局限性，基于光纤的方法无法实现全球尺度下的纠缠分发。本文研究了一种名为 QuESat 的新型天地混合量子网络架构，用于实现全球尺度的纠pre缠分发。该架构将地面光纤网络与一个由低地球轨道（LEO）卫星构建的全球尺度无源光网络（Passive Optical Network）相结合。该卫星网络能够通过可调节的透镜阵列构建近真空光束导引，从而动态地建立光子光路（lightpath）。与使用光纤相比，这种方式能以极高的效率将光子从一个地面站远距离转发至另一个。

为评估 QuESat 在全球通信中的可行性与有效性，我们构建了光路配置（lightpath provisioning）和纠缠分发问题模型，其中考虑了卫星的轨道动力学以及来自地面用户的时变纠缠需求。我们为此开发了一种两阶段算法，分别用于动态地配置光束导引和分发纠缠。该算法将用于光路配置的随机化与确定性取整（randomized and deterministic rounding）方法相结合以实现全球连通性，并采用最优的纠缠交换（entanglement swapping）策略来分发纠缠以满足用户需求。通过开发一个天地混合量子网络模拟器，我们验证了 QuESat 相比于传统（量子）中继网络，能够在性能上实现数倍的提升。

Introduction

Entanglement distribution over remote distances is essential to many applications such as quantum key distribution (QKD) [5], distributed quantum computing (DQC) [8], [13], and quantum internet-of-things [11]. Current approaches mainly rely on optical fiber as light guides for entangled photons due to its flexibility, relatively low cost of deployment (compared to alternative approaches), and existing large-scale deployment. However, exponential photon loss in fiber hinders single photon transmission as distances increase, limiting the practical range of such networks to a few hundred kilometers [35], [40].

To overcome this limitation, the first-generation quantum networks aim to utilize quantum repeaters to enable long-distance entanglement distribution [18]. A quantum repeater concatenates short-distance entanglements to generate longerdistance ones via entanglement swapping, and performs optional entanglement distillation to improve fidelity, with the help of quantum memories and measurement devices [41], [48], [54]. While promising quantum repeaters have two limiting factors. First, their effectiveness is limited by the current low efficiency of memory and measurement devices, which degrades exponentially as more repeaters are needed to establish longer-distance entanglements. Second, quantum memory and measurement devices are particularly expensive and energyhungry (including the need for cryostat for several candidate memory technologies), making them particularly costly and challenging to deploy and operate.

This paper investigates and proposes a new architecture for achieving global-scale entanglement distribution with ultra high efficiency. The architecture features, in addition to the ground fiber network, a satellite-assisted passive optical network for directly transmitting entangled photons between arbitrary ground stations. As shown in Fig. 1, each satellite is equipped with reflecting or refracting lenses, such that a sequence of lenses forms a free-space lightpath directly from the sender to the receiver for photon transmission. To distribute an entanglement, the entanglement source (assumed to be at a ground station) generates entangled photon pairs, and sends one photon in each pair along the pre-configured lightpath directly to the receiver (another ground station). Each satellite along the path simply reflects or refracts the photon stream without performing any operation, thereby removing the reliance on any expensive and energy-hungry memory or measurement device in space. Furthermore, compared to fiber, such a free-space lightpath can have orders of magnitude lower loss (mainly due to reflection/refraction) at long distances, for instance, less than 10 −3 to 10 −4 dB/km compared to 0.2dB/km for fiber [19], [22], [52]. With a constellation of cost-efficient low-Earth-orbit (LEO) satellites covering the planet, and shortdistance ground fiber connecting ground stations to nearby users, this architecture can provide highly-efficient and low-cost entanglement distribution over very long distances with currently available and near-term quantum technologies.

Compared to a repeater network based on swapping and/or distillation, the satellite passive optical network relies on pure mechanical operations—aligning the lenses for properly reflecting or refracting to the next hop/destination. This prompts a new design problem of provisioning lightpaths to satisfy end-to-end entanglement needs. Entanglements distributed over these lightpaths and/or via ground fiber can further be swapped by ground repeaters (e.g., co-located at the ground stations) to build entanglements between users or other ground stations who do not have an available lightpath. The combined problem of lightpath provisioning and entanglement distribution becomes non-trivial and has no counterpart in either classical optical networks or quantum repeater networks alone. To this end, we provide a formulation of this problem and then develop a two-stage algorithm to dynamically reconfigure satellite lightpaths based on satellite orbital dynamics, as well as to schedule swapping operations at repeaters to satisfy users’ entanglement demands. We further develop a hybrid ground-satellite quantum network simulator based on known satellite orbits. Utilizing our algorithm and simulator, and combining existing simulation and experimental data, we evaluate the performance of the proposed hybrid architecture, and demonstrate that it achieves multifold improvements in entanglement rate and users’ demand satisfaction compared to a fiber-based repeater network.

Our main contributions are as follows:

• We propose a novel quantum network architecture that distributes highly efficient entanglements at a global scale through a combination of a ground repeater network and a satellite-assisted passive optical network without memories or measurement devices. The satellite network is implementable with current/near-term technologies as demonstrated by recent breakthroughs [19], [22].

• We formulate the lightpath provisioning and entanglement distribution problems in this hybrid ground-satellite architecture and develop a two-stage algorithm considering both the orbital dynamics of satellites and the dynamic demand changes of ground users.

• We develop a ground-satellite quantum network simulator, and use real satellite traces to demonstrate that the hybrid architecture can achieve multi-fold improvement in entanglement rate and demand satisfaction compared to ground repeater networks only with fiber.

Organization. §II introduces background and related work. §III shows preliminaries for entanglement distribution in a satellite-assisted quantum network. §IV presents the network model and problem formulation. §V proposes the two-stage algorithm design for entanglement distribution in QuESat. §VI presents evaluation results. §VII is the conclusion.

跨越长距离的纠缠分发对于诸如量子密钥分发（QKD）[5]、分布式量子计算（DQC）[8], [13]以及量子物联网[11]等众多应用至关重要。当前的方法主要依赖光纤作为纠缠光子的光导，因其具有灵活性、相对较低的部署成本（与其他替代方案相比）以及已存在的大规模部署。然而，光纤中指数级的光子损耗阻碍了单光子随距离的增加而传输，从而将此类网络的实际有效范围限制在几百公里之内[35], [40]。

为克服这一限制，第一代量子网络旨在利用量子中继来实现长距离的纠缠分发[18]。量子中继借助量子存储器和测量设备，通过纠缠交换将短距离的纠缠级联以生成长距离的纠缠，并执行可选的纠缠提纯来提高保真度[41], [48], [54]。尽管量子中继前景广阔，但它存在两个限制因素。首先，其有效性受到当前存储器和测量设备效率低下的限制，当需要更多中继来建立更长距离的纠缠时，这种效率会呈指数级下降。其次，量子存储器和测量设备尤其昂贵且高能耗（例如，数种候选的存储技术需要低温恒温器），这使得它们的部署和运营成本极高且极具挑战性。

本文研究并提出了一种旨在实现全球尺度、超高效率纠缠分发的新型架构。该架构的特点是，在地面光纤网络之外，增加了一个卫星辅助的无源光网络，用于在任意地面站之间直接传输纠缠光子。如图1所示，每颗卫星都配备了反射或折射透镜，这样一系列透镜便能形成一条从发送方到接收方的自由空间光路，用于光子传输。为分发一段纠缠，纠缠源（假设位于某个地面站）生成纠缠光子对，并将每对中的一个光子沿预先配置好的光路直接发送给接收方（另一个地面站）。路径上的每颗卫星仅对光子流进行反射或折射，不执行任何操作，从而摆脱了对太空中任何昂贵且高能耗的存储器或测量设备的依赖。此外，与光纤相比，这种自由空间光路在长距离上的损耗要低几个数量级（主要由反射/折射引起），例如，其损耗低于10⁻³至10⁻⁴ dB/公里，而光纤为0.2dB/公里[19], [22], [52]。通过一个由高性价比的低地球轨道（LEO）卫星组成的星座覆盖全球，并利用短距离的地面光纤连接地面站与邻近用户，该架构能够利用现有及近期可实现的量子技术，在极长距离上提供高效且低成本的纠缠分发。

与基于（纠缠）交换和/或提纯的中继网络相比，该卫星无源光网络依赖于纯粹的机械操作——调整透镜以恰当地将光子反射或折射至下一跳/目的地。这催生了一个全新的设计问题：配置光路（provisioning lightpaths）以满足端到端的纠缠需求。通过这些光路和/或地面光纤分发的纠缠，可以被地面中继（例如，与地面站部署在同一位置）进一步交换，以便在没有可用光路的用户或其他地面站之间建立纠缠。这个光路配置与纠缠分发的组合问题是一个非平凡（non-trivial）的问题，在传统的经典光网络或单纯的量子中继网络中都没有对应物。为此，我们对该问题进行了形式化构建，并进而开发了一种两阶段算法，以根据卫星的轨道动力学动态地重构卫星光路，并调度中继处的交换操作以满足用户的纠缠需求。我们进一步开发了一个天地混合量子网络模拟器，并结合已知的卫星轨道数据，利用我们的算法和模拟器，并整合现有的仿真与实验数据，对所提出的混合架构的性能进行了评估。评估结果表明，与基于光纤的中继网络相比，该架构在纠缠速率和用户需求满足率方面实现了数倍的性能提升。

我们的主要贡献如下：

  • 我们提出了一种新颖的量子网络架构，该架构通过结合地面中-继网络和一个无需存储器或测量设备的卫星辅助无源光网络，在全球尺度上高效地分发纠缠。最近的突破性进展[19], [22]表明，该卫星网络可利用当前/近期技术实现。
  • 我们构建了在这种天地混合架构下的光路配置和纠缠分发问题模型，并开发了一种两阶段算法，该算法同时考虑了卫星的轨道动力学和地面用户的动态需求变化。
  • 我们开发了一个天地混合量子网络模拟器，并使用真实的卫星轨迹数据证明，与仅有地面光纤的中继网络相比，该混合架构在纠缠速率和需求满足率方面能够实现数倍的提升。

文章结构。 第II节介绍研究背景与相关工作。第III节阐述在星地协同量子网络中进行纠缠分发所需的预备知识。第IV节给出网络模型并进行问题构建。第V节提出在QuESat中用于纠缠分发的两阶段算法设计。第VI节展示评估结果。第VII节为全文总结。