We develop a protocol for entanglement generation in the quantum internet that allows a repeater node to use
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Abstract n qubit GreenbergerHorneZeilinger (GHZ) projective measurements that can fusen successfully entangledlinks , i.e., twoqubit entangled Bell pairs shared acrossn network edges, incident at that node. Implementingn fusion, forn ≥ 3, is in principle not much harder than 2fusions (Bellbasis measurements) in solidstate qubit memories. If we allow even 3fusions at the nodes, we find—by developing a connection to a modified version of the sitebond percolation problem—that despite lossy (hence probabilistic) linklevel entanglement generation, and probabilistic success of the fusion measurements at nodes, one can generate entanglement between end parties Alice and Bob at a rate that stays constant as the distance between them increases. We prove that this powerful network property is not possible to attain with any quantum networking protocol built with Bell measurements and multiplexing alone. We also design a twoparty quantum key distribution protocol that converts the entangled states shared between two nodes into a shared secret, at a key generation rate that is independent of the distance between the two parties. 
We study a quantum entanglement distribution switch serving a set of users in a star topology with equallength links. The quantum switch, much like a quantum repeater, can perform entanglement swapping to extend entanglement across longer distances. Additionally, the switch is equipped with entanglement switching logic, enabling it to implement switching policies to better serve the needs of the network. In this work, the function of the switch is to create bipartite or tripartite entangled states among users at the highest possible rates at a fixed ratio. Using Markov chains, we model a set of randomized switching policies. Discovering that some are better than others, we present analytical results for the case where the switch stores one qubit per user, and find that the best policies outperform a time division multiplexing policy for sharing the switch between bipartite and tripartite state generation. This performance improvement decreases as the number of users grows. The model is easily augmented to study the capacity region in the presence of quantum state decoherence and associated cutoff times for qubit storage, obtaining similar results. Moreover, decoherenceassociated quantum storage cutoff times appear to have little effect on capacity in our identicallink system. We also study a smaller class of policies when the switch stores two qubits per user.more » « lessFree, publiclyaccessible full text available June 30, 2024

Recent technological advancements in satellite based quantum communication has made it a promising technology for realizing global scale quantum networks. Due to better loss distance scaling compared to ground based fiber communication, satellite quantum communication can distribute high quality quantum entanglements among ground stations that are geographically separated at very long distances. This work focuses on optimal distribution of bipartite entanglements to a set of pair of ground stations using a constellation of orbiting satellites. In particular, we characterize the optimal satellitetoground station transmission scheduling policy with respect to the aggregate entanglement distribution rate subject to various resource constraints at the satellites and ground stations. We cast the optimal transmission scheduling problem as an integer linear programming problem and solve it efficiently for some specific scenarios. Our framework can also be used as a benchmark tool to measure the performance of other potential transmission scheduling policies.more » « less

Hemmer, Philip R. ; Migdall, Alan L. (Ed.)We study a quantum switch that creates shared endtoend entangled quantum states to multiple sets of users that are connected to it. Each user is connected to the switch via an optical link across which bipartite Bellstate entangled states are generated in each timeslot with certain probabilities, and the switch merges entanglements of links to create endtoend entanglements for users. One qubit of an entanglement of a link is stored at the switch and the other qubit of the entanglement is stored at the user corresponding to the link. Assuming that qubits of entanglements of links decipher after one timeslot, we characterize the capacity region, which is defined as the set of arrival rates of requests for endtoend entanglements for which there exists a scheduling policy that stabilizes the switch. We propose a MaxWeight scheduling policy and show that it stabilizes the switch for all arrival rates that lie in the capacity region. We also provide numerical results to support our analysis.more » « less

In a quantum network that successfully creates links—shared Bell states between neighboring repeater nodes—with probability p in each time slot, and performs Bell State Measurements at nodes with success probability q < 1, the endtoend entanglement generation rate drops exponentially with the distance between consumers, despite multipath routing. If repeaters can perform multiqubit projective measurements in the GHZ basis that succeed with probability q, the rate does not change with distance in a certain (p,q) region, but decays exponentially outside. This region where the distanceindependent rate occurs is the supercritical region of a new percolation problem. We extend this GHZ protocol to incorporate a timemultiplexing blocklength k, the number of time slots over which a repeater can mixandmatch successful links to perform fusion on. As k increases, the supercritical region expands. For a given (p,q), the entanglement rate initially increases with k, and once inside the supercritical region for a high enough k, it decays as 1/k GHZ states per time slot. When memory coherence time exponentially distributed with mean μ is incorporated, it is seen that increasing k does not indefinitely increase the supercritical region; it has a hard μdependent limit. Finally, we find that incorporating spacedivision multiplexing, i.e., running the above protocol independently in up to d disconnected network regions, where d is the network’s node degree, one can go beyond the 1 GHZ state per time slot rate that the above randomized locallinkstate protocol cannot surpass. As (p,q) increases, one can approach the ultimate mincut entanglementgeneration capacity of d GHZ states per slot.more » « less

Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum computation among quantum computers. In this work, we describe a quantum walk protocol to perform distributed quantum computing in a quantum network. The protocol uses a quantum walk as a quantum control signal to perform distributed quantum operations. We consider a generalization of the discretetime coined quantum walk model that accounts for the interaction between a quantum walker system in the network graph with quantum registers inside the network nodes. The protocol logically captures distributed quantum computing, abstracting hardware implementation and the transmission of quantum information through channels. Control signal transmission is mapped to the propagation of the walker system across the network, while interactions between the control layer and the quantum registers are embedded into the application of coin operators. We demonstrate how to use the quantum walker system to perform a distributed CNOT operation, which shows the universality of the protocol for distributed quantum computing. Furthermore, we apply the protocol to the task of entanglement distribution in a quantum network.more » « less