The primary task of a quantum repeater network is to deliver entanglement among end nodes. Most of existing entanglement distribution protocols do not consider purification, which is thus delegated to an upper layer. This is a major drawback since, once an end-to-end entangled connection (or a portion thereof) is established it cannot be purified if its fidelity (F) does not fall within an interval bounded by Fmin (greater than 0.5) and Fmax (less than 1). In this paper, we propose the Ranked Entanglement Distribution Protocol (REDiP), a connection-oriented protocol that overcomes the above drawback. This result was achieved by including in our protocol two mechanisms for carrying out jointly purification and entanglement swapping. We use simulations to investigate the impact of these mechanisms on the performance of a repeater network, in terms of throughput and fidelity. Moreover, we show how REDiP can easily be configured to implement custom entanglement swapping and purification strategies, including (but not restricted to) those adopted in two recent works.
The primary task of a quantum repeater network is to deliver entanglement among end nodes. Most of existing entanglement distribution protocols do not consider purification, which is thus delegated to an upper layer. This is a major drawback since, once an end-to-end entangled connection (or a portion thereof) is established it cannot be purified if its fidelity (F) does not fall within an interval bounded by Fmin (greater than 0.5) and Fmax (less than 1). In this paper, we propose the Ranked Entanglement Distribution Protocol (REDiP), a connection-oriented protocol that overcomes the above drawback. This result was achieved by including in our protocol two mechanisms for carrying out jointly purification and entanglement swapping. We use simulations to investigate the impact of these mechanisms on the performance of a repeater network, in terms of throughput and fidelity. Moreover, we show how REDiP can easily be configured to implement custom entanglement swapping and purification strategies, including (but not restricted to) those adopted in two recent works.
The distribution of entangled qubit pairs to end nodes is the key requirement of a quantum network to enable qubit state transmission through quantum teleportation. Existing protocols for entanglement distribution fix a specific swapping order on the involved quantum repeaters and delegate entanglement purification to upper-layer protocols. This limitation is problematic because entangled states tend to degrade due to quantum noise, and they cannot be purified if their fidelity (i.e. quality) falls below a certain threshold. It is therefore of the utmost importance to co-plan entanglement swapping and purification to achieve a target end-to-end fidelity. In this work, we present the Ranked Entanglement Distribution Protocol (REDiP), which overcomes the aforementioned limits by including the "ranks" mechanism to configure the ordering of both purification and entanglement swapping steps. We show how REDiP can easily be configured to implement custom entanglement swapping and purification strategies, including (but not restricted to) those adopted in two recent works. We also propose an algorithm to estimate the bandwidth to allocate on every link of the REDiP path, and we provide a set of guidelines on how REDiP ranks can be configured depending on user requirements and hardware configuration. Such guidelines are driven by original insights into purification performance. We conduct simulations to verify our results and assess the impact of different REDiP configurations on the performance of a repeater network, in terms of throughput and fidelity.
When built, quantum repeater networks will require classical network protocols to control the quantum operations. However, existing work on repeaters has focused on the quantum operations themselves, with less attention paid to the contents, semantics, ordering and reliability of the classical control messages. In this work we define and describe our implementation of the classical control protocols. The state machines and packet sequences for the three protocol layers are presented, and operation confirmed by running the protocols over simulations of the physical network. We also show that proper management of the resources in a bottleneck link allows the aggregate throughput of two end-to-end flows to substantially exceed that of a single flow. Our layered architectural framework will support independent evolution of the separate protocol layers. Networks of quantum repeaters utilize three concepts to execute a distributed algorithm that creates entangled quantum states between nodes that are far apart: a basic entanglement mechanism which depends on the physical implementation, error management (in this work, we study a method known as purification), and finally a quantum state propagation layer (here we implement entanglement swapping, which builds multi-hop connections from single-hop connections). Some researchers are investigating approaches that are substantially different from entanglement swapping [30, 24, 19]. Here we focus on swapping, but the layered architecture approach is broadly applicable, allowing other implementations to replace only a single layer in the protocol stack. Previous work primarily focused on the physical and mathematical tools for building repeaters. Classical information is also needed to enable teleportation and swapping, as many quantum operations are not deterministic, and results of quantum measurements need to be reported to distant partners before further operations can proceed. Also, operations in the middle of the network must be coordinated to route and swap properly. This requires classical messages to make operations robust, but message propagation times penalize performance. Even though this delay is usually included in repeater simulations, prior work has not defined the protocols in detail, especially with respect to how all of the nodes make consistent decisions in a timely fashion. In this work, we introduce a protocol stack for networks of quantum repeaters that considers all the necessary classical messages and which can be easily adapted for different approaches at all three protocol layers. We run simulations of competing flows on a dumbbell topology in order to increase our confidence in the behavior of our network protocols. By adjusting the fidelity thresholds required for entanglement swapping, we show that some configurations boost the aggregate throughput for multiple flows significantly above the maximum for a single flow, taking advantage of resources that would otherwise sit idle. The operation of such complex networks and such delicate tuning of the system without formal protocol definitions would not be possible. Previous work has also concentrated almost exclusively on the dedicated use of a single line or chain of repeaters, delivering Bell pairs only to the two nodes at the ends of the chain. Networks, however, typically have more than two end points, and allow any pair of these end nodes to communicate. More topologically complex networks, with numerous end nodes, are obviously much more scalable than connecting every possible pair of nodes using a dedicated line of repeaters. we investigate how classical multiplexing schemes translate to the domain of quantum repeaters, in order to manage shared resources and active communication flows of data from different stations. We simulate four sharing protocols in a complex network with competing traffic. Circuit switching gives any individual flow the best performance, but makes poor use of the overall network and is inflexible. We use circuit switching as our baseline case to compare time division multiplexing, buffer space multiplexing, and statistical multiplexing, and show that all multiplexing schemes are better than circuit switching. For the particular network simulated, we find that statistical multiplexing outperforms time division multiplexing by 28% and buffer space multiplexing by 13%. We find that all three multiplexing schemes are fair; each flow is penalized a similar percentage of its throughput as the the total number of users in the network increases. Finally, statistical multiplexing requires no network-wide coordination of the use of quantum memory or channels, and is easier to implement than a robust, scalable scheme for the other protocols. Our current results suggest that the best strategy for quantum repeater networks is statistical multiplexing. (This is in fact the quantum analogue of the basis on which the Internet works.) However, our current simulations are done with no degradation of memory over time, using the assumption of quantum error-corrected memory at each repeater; inclusion of decoherence and a finite qubit lifetime remains as future work.
Entanglement-based quantum networks can provide unconditionally secure communication by distributing entangled pairs between distant end nodes. To achieve end-to-end entanglement distribution, multiple operations of entanglement swapping in a quantum repeater chain are always required. However, due to the non-determinism of entanglement swapping caused by imperfect physical devices, the execution pattern of swapping operations has a direct impact on the performance of entanglement distribution, which can be categorized into an entanglement access control (EAC) problem. In this article, we attribute the EAC problem to two aspects: the matching optimization within quantum nodes, and the swapping conflict avoidance between quantum nodes. Accordingly, we propose an asynchronous entanglement distribution protocol which contains a custom weighted maximum matching algorithm, and a reliable signaling interaction mechanism to avoid a swapping conflict, respectively. Based on the proposed protocol, quantum repeaters autonomously decide their behaviors and spontaneously construct the end-to-end entangled pairs asynchronously. Simulation results show that our protocol can significantly improve the entanglement distribution rate and fidelity of end-to-end entangled pairs while simplifying the deployment and management process of the quantum networks.
Quantum network is a promising platform for numerous quantum applications, including distributed quantum computing, secure communication, and improved sensing. Implementing entanglement distribution between remote quantum nodes plays a vital role in realizing the quantum network's capabilities, and it requires effective remote entanglement distribution protocols. To meet this requirement, we propose two strategies, namely connection-oriented and connectionless, to achieve end-to-end entanglement distribution inspired by the designs of classical communication. For the connection-oriented strategy, an exclusive quantum connection is pre-established between the source and destination nodes. For the connectionless strategy, entanglement swapping is performed hop-by-hop tentatively. In this way, the best-effort service is provided for the source node to establish long-distance entanglement with the destination node. Analogous to classical communication, the proposed strategies have their advantages and disadvantages. Our simulation results show that the connectionless strategy is more efficient and robust than the connection-oriented strategy in terms of throughput. However, the connection-oriented strategy provides reliable end-to-end entanglement distribution but at the expense of higher overhead. Moreover, the application scenarios of these two strategies are discussed. This work paves the road for designing end-to-end entanglement distribution protocols in quantum networks.
Swapping and purification are the two fundamental building blocks for high-fidelity entanglement distribution in multi-hop quantum networks. Unfortunately, it is still a mystery how they intertwine with each other to affect the fidelity and cost of end-to-end entanglements. Current scheduling algorithms consider this problem under relatively limited assumptions and a critical yet unjustified conjecture. In this work, we first consider more general assumptions with operation failures and, accordingly, extend a tree-based modeling for joint swapping and purification. Then, we analytically prove the previous conjecture that the optimal strategy underBinary systemis always to purify the entanglements before any swapping. This sheds light on the protocol and device design for quantum networks. We then further propose a tree-based algorithm, which can efficiently schedule swapping and purification along a path for bothBinaryandWerner systems. Extensive simulations of the proposed method against state-of-the-art solutions show that our method uses fewer entanglements to establish qualified end-to-end entanglements, and thus achieves higher network throughput.
Quantum repeater networks that allow long-distance entanglement distribution will be the backbone of distributed quantum information processing. In this paper we explore entanglement distribution using quantum repeaters with optimized buffer time, equipped with noisy quantum memories and performing imperfect entanglement purification and swapping. We observe that increasing the number of memories on end nodes leads to a higher entanglement distribution rate per memory and higher probability of high-fidelity entanglement distribution, at least for the case with perfect operations. When imperfect operations are considered, however, we make the surprising observation that the permemory entanglement rate decreases with increasing number of memories. Our results suggest that building quantum repeaters that perform well under realistic conditions requires careful modeling and design that takes into consideration the operations and resources that are finite and imperfect.