We propose some protocols to implement various classes of bipartite unitary operations on two remote parties with the help of repeater nodes in-between. We also present a protocol to implement a single-qubit unitary with parameters determined by a remote party with the help of up to three repeater nodes. It is assumed that the neighboring nodes are connected by noisy photonic channels, and the local gates can be performed quite accurately, while the decoherence of memories is significant. A unitary is often a part of a larger computation or communication task in a quantum network, and to reduce the amount of decoherence in other systems of the network, we focus on the goal of saving the total time for implementing a unitary including the time for entanglement preparation. We review some previously studied protocols that implement bipartite unitaries using local operations and classical communication and prior shared entanglement, and apply them to the situation with repeater nodes without prior entanglement. We find that the protocols using piecewise entanglement between neighboring nodes often require less total time compared to preparing entanglement between the two end nodes first and then performing the previously known protocols. For a generic bipartite unitary, as the number of repeater nodes increases, the total time could approach the time cost for direct signal transfer from one end node to the other. We also prove some lower bounds of the total time when there are a small number of repeater nodes. The application to position-based cryptography is discussed.
We propose some protocols to implement various classes of bipartite unitary operations on two remote parties with the help of repeater nodes in-between. We also present a protocol to implement a single-qubit unitary with parameters determined by a remote party with the help of up to three repeater nodes. It is assumed that the neighboring nodes are connected by noisy photonic channels, and the local gates can be performed quite accurately, while the decoherence of memories is significant. A unitary is often a part of a larger computation or communication task in a quantum network, and to reduce the amount of decoherence in other systems of the network, we focus on the goal of saving the total time for implementing a unitary including the time for entanglement preparation. We review some previously studied protocols that implement bipartite unitaries using local operations and classical communication and prior shared entanglement, and apply them to the situation with repeater nodes without prior entanglement. We find that the protocols using piecewise entanglement between neighboring nodes often require less total time compared to preparing entanglement between the two end nodes first and then performing the previously known protocols. For a generic bipartite unitary, as the number of repeater nodes increases, the total time could approach the time cost for direct signal transfer from one end node to the other. We also prove some lower bounds of the total time when there are a small number of repeater nodes. The application to position-based cryptography is discussed.
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.
Scaling the number of entangled nodes in a quantum network is a challenge with significant implications for quantum computing, clock synchronisation, secure communications, and quantum sensing. In a quantum network, photons interact with matter qubits at different nodes, flexibly enabling the creation of remote entanglement between them. Multipartite entanglement among multiple nodes will be crucial for many proposed quantum network applications, including quantum computational tasks and quantum metrology. To date, experimental efforts have primarily focused on generating bipartite entanglement between nodes, which is widely regarded as the fundamental quantum resource for quantum networks. However, relying exclusively on bipartite entanglement to form more complex multipartite entanglement introduces several challenges. These include the need for ancillary qubits, extensive local entangling operations which increases the preparation latency, and increasingly stringent requirements on coherence times as the number of nodes grows. Here, we analyse various schemes that achieve multipartite entanglement between nodes in a single step, bypassing the need for multiple rounds of bipartite entanglement. We demonstrate that different schemes can produce distinct multipartite entangled states, with varying fidelity and generation rates. Additionally, we discuss the applicability of these schemes across different experimental platforms, highlighting their primary advantages and disadvantages.
We present a method of optimizing recently designed protocols for implementing an arbitrary nonlocal unitary gate acting on a bipartite system. These protocols use only local operations and classical communication with the assistance of entanglement, and they are deterministic while also being ``one-shot,'' in that they use only one copy of an entangled resource state. The optimization minimizes the amount of entanglement needed, and also the amount of classical communication, and it is often the case that less of each of these resources is needed than with an alternative protocol using two-way teleportation.
In certain cases the communication time required to deterministically implement a nonlocal bipartite unitary using prior entanglement and local operations and classical communication can be reduced by a factor of two. We introduce two such ``fast'' protocols and illustrate them with various examples. For some simple unitaries, the entanglement resource is used quite efficiently. The problem of exactly which unitaries can be implemented by these two protocols remains unsolved, though there is some evidence that the set of implementable unitaries may expand at the cost of using more entanglement.
Future communication systems are expected to integrate quantum networks to enable highly secure communication and enhance computational capabilities. In quantum networks, communication is accomplished by sharing entanglement between remote locations, which is the basis for most known quantum protocols. Entanglement is a correlation between qubits that is not reproducible with classical means. However, as entanglement is susceptible to noise limiting its range, quantum repeaters can enable entanglement over more considerable distances. Using the entanglement swapping protocol, quantum repeaters can be placed between remote locations to establish entanglement. This requires each repeater to first generate entanglement with its neighboring nodes, named entanglement generation. However, as the size of current quantum networks is limited, the development and evaluation of quantum networks and quantum protocols is based on simulations. To simulate quantum networks accurately, accurate and high-performance models of the entanglement generation process must be employed. This paper proposes two new models for generating entanglement in simulations and develops quantum protocols for generating and purifying entanglement. The protocols are evaluated in thorough simulations under perfect and realistic conditions regarding delay and fidelity. Furthermore, the accuracy and runtime of the models are evaluated. The results show the models are accurate, with delay primarily influenced by the source duration, while longer coherence times significantly enhance fidelity. The model runtimes are consistently shorter than the simulation runtimes across all protocols, averaging about 2% of the total simulation time.
Emerging communication systems are expected to integrate new types of communication networks including quantum networks. In contrast to classical networks, the communication in quantum networks is accomplished with qubits and their attribute entanglement. Entanglement is a type of correlation between multiple qubits with no counterpart in classical communication. With the help of entanglement new protocols are developed to perform classical and quantum network tasks more efficiently. The main task of quantum networks is to share entanglement to distant communication partners with the help of intermediate nodes and repeated entanglement swapping, the so called Repeater Protocol. Due to the decoherence of quantum states, establishing entanglement has to be accomplished with minimal delay to preserve the states of qubits. This paper proposes a new Repeater Protocol FRP, which reduces delay by up to 51% and on average by 13% in establishing end-to-end entanglement compared with the direct approach CRP. Additionally, the provided solution lowers hardware requirements for quantum routers. Both protocols, CRP and FRP are evaluated in terms of end-to-end delay and fidelity in extensive simulations with a parameter search on 3 different topologies.