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.
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.
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.
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.
Complex quantum networks can support a diverse set of long-range entanglement distribution schemes ranging from linear repeater protocols to multipath entanglement purification strategies. As a result, a network's resourcefulness, that is its ability to facilitate quantum communication, depends on the deployed distribution scheme. In this work, we analyse and compare the resourcefulness of quantum networks across a broad range of network topologies, including both regular and random networks, under two distinct entanglement distribution schemes. The first relies on entanglement swapping along a single path connecting a source-target pair, while the second exploits entanglement purification using multiple paths between the same source and target nodes. The resourcefulness of the network is quantified using a recently described metric [1] that averages over the maximum teleportation fidelity between arbitrary source-target pairs in the network. We present algorithms for estimating this metric under constraints of edge-usage and ordering of paths. Our results not only demonstrate the sensitivity of the average maximum teleportation fidelity metric to the choice of entanglement distribution protocol, but also highlight the significant improvements enabled by network purification schemes. In particular, purification-based approaches can substantially enhance average teleportation fidelity, thereby improving the overall teleportation capability of quantum networks.
We study quantum entanglement distribution on networks with full-rank bi-partite mixed states linking qubits on nodes. In particular, we use entanglement swapping and purification to partially entangle widely separated nodes. The simplest method consists of performing entanglement swappings along the shortest chain of links connecting the two nodes. However, we show that this method may be improved upon by choosing a protocol with a specific ordering of swappings and purifications. A priori, the design that produces optimal improvement is not clear. However, we parametrize the choices and find that the optimal values depend strongly on the desired measure of improvement. As an initial application, we apply the new improved protocols to the Erdös--Rényi network and obtain results including low density limits and an exact calculation of the average entanglement gained at the critical point.
Quantum information technology has the potential to revolutionize computing, communications, and security. To fully realize its potential, quantum processors with millions of qubits are needed, which are still far from being accomplished. Thus, it is important to establish quantum networks to enable distributed quantum computing to leverage existing and near-term quantum processors into more powerful resources. This paper proposes an efficient entanglement distribution protocol for classical-quantum networks with a limited number of quantum links, enabling quantum teleportation in near-term hybrid networks. The proposed protocol uses entanglement swapping and classical network coding to distribute entanglements efficiently while overcoming bottlenecks and minimizing qubit and link usage. Experimental results show that the proposed protocol requires quantum resources that scale linearly with network size, with individual nodes only requiring a fixed number of qubits. For small network sizes of up to three transceiver pairs, the proposed protocol outperforms the benchmark by using 17% fewer qubit resources, achieving 8.8% higher accuracy, and with a 35% faster simulation time. The percentage improvement increases significantly for large network sizes. We also propose a protocol for securing entanglement distribution against malicious entanglements using quantum state encoding through rotation. Our analysis shows that this method requires no communication overhead and reduces the chance of a malicious node retrieving the teleported state to 7.2%. The achieved results point toward a protocol that enables a highly scalable, efficient, and secure near-term quantum Internet.
We study quantum entanglement distribution on networks with full-rank bi-partite mixed states linking qubits on nodes. In particular, we use entanglement swapping and purification to partially entangle widely separated nodes. The simplest method consists of performing entanglement swappings along the shortest chain of links connecting the two nodes. However, we show that this method may be improved upon by choosing a protocol with a specific ordering of swappings and purifications. A priori, the design that produces optimal improvement is not clear. However, we parameterize the choices and find that the optimal values depend strongly on the desired measure of improvement. As an initial application, we apply the new improved protocols to the Erd\"os--R\'enyi network and obtain results including low density limits and an exact calculation of the average entanglement gained at the critical point.