We study a quantum entanglement distribution switch serving a set of users in a star topology with equal-length 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 cut-off times for qubit storage, obtaining similar results. Moreover, decoherence-associated quantum storage cut-off times appear to have little effect on capacity in our identical-link system. We also study a smaller class of policies when the switch stores two qubits per user.We study a quantum entanglement distribution switch serving a set of users in a star topology with equal-length 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 cut-off times for qubit storage, obtaining similar results. Moreover, decoherence-associated quantum storage cut-off times appear to have little effect on capacity in our identical-link system. We also study a smaller class of policies when the switch stores two qubits per user.

ACM Transactions on Modeling and Performance Evaluation of Computing SystemsNov 19, 202217 citations

On the Capacity Region of Bipartite and Tripartite Entanglement Switching

Gayane Vardoyan, Saikat Guha, Philippe Nain +1 more

We study a quantum switch serving a set of users in a star topology. The function of the switch is to create bipartite or tripartite entangled state among users at the highest possible rates at a fixed ratio. 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 (TDM) 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 qubit decoherence, obtaining similar results. Moreover, decoherence appears to have little effect on capacity. We also study a smaller class of policies when the switch stores two qubits per user.We study a quantum switch serving a set of users in a star topology. The function of the switch is to create bipartite or tripartite entangled state among users at the highest possible rates at a fixed ratio. 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 (TDM) 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 qubit decoherence, obtaining similar results. Moreover, decoherence appears to have little effect on capacity. We also study a smaller class of policies when the switch stores two qubits per user.

ACM SIGMETRICS Performance Evaluation ReviewMar 5, 202122 citations

On the Capacity Region of Bipartite and Tripartite Entanglement Switching and Key Distribution

Gayane Vardoyan, Saikat Guha, Philippe Nain +1 more

We study a quantum switch serving a set of users. The function of the switch is to convert bipartite entanglement generated over individual links connecting each user to the switch, into bipartite or tripartite entangled states among (pairs or groups of) users at the highest possible rates at a fixed ratio. Such entanglement can then be converted to quantum-secure shared secret bits among pairs or triples of users using E91-like Quantum Key Distribution (QKD) protocols. The switch can store a certain number of qubits in a quantum memory for a certain length of time, and can make two-qubit Bell-basis measurements or three-qubit GHZ-basis projective measurements on qubits held in the memory. 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 at a given time step, and find that the best policies outperform a time division multiplexing (TDM) policy for sharing the switch between bipartite and tripartite entanglement 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 qubit decoherence, obtaining similar results. Moreover, decoherence appears to have little effect on capacity. We also study a smaller class of policies when the switch can store two qubits per user. The full manuscript can be found at https://arxiv.org/abs/1901.06786.We study a quantum switch serving a set of users. The function of the switch is to convert bipartite entanglement generated over individual links connecting each user to the switch, into bipartite or tripartite entangled states among (pairs or groups of) users at the highest possible rates at a fixed ratio. Such entanglement can then be converted to quantum-secure shared secret bits among pairs or triples of users using E91-like Quantum Key Distribution (QKD) protocols. The switch can store a certain number of qubits in a quantum memory for a certain length of time, and can make two-qubit Bell-basis measurements or three-qubit GHZ-basis projective measurements on qubits held in the memory. 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 at a given time step, and find that the best policies outperform a time division multiplexing (TDM) policy for sharing the switch between bipartite and tripartite entanglement 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 qubit decoherence, obtaining similar results. Moreover, decoherence appears to have little effect on capacity. We also study a smaller class of policies when the switch can store two qubits per user. The full manuscript can be found at https://arxiv.org/abs/1901.06786.

Aug 26, 20190 citations

On the Stochastic Analysis of a Quantum Entanglement Distribution Switch

Gayane Vardoyan, Saikat Guha, Philippe Nain +1 more

In this article, we study a quantum entanglement distribution switch that serves $k$ users in a star topology. We model variants of the system as continuous-time Markov chains and obtain expressions for switch capacity, expected number of qubits stored in memory at the switch, and the quantum memory occupancy distribution. We obtain a number of analytic results for systems in which measurements are imperfect, the links are homogeneous or heterogeneous and for switches that have an infinite or finite number of quantum memories or buffers. In addition, we model the effect of decoherence of quantum states and associated cutoff times on their storage using a simple model. From numerical observations, we discover that decoherence-associated cutoff times have little effect on capacity and expected number of stored qubits for homogeneous systems. For heterogeneous systems, especially those operating near the boundaries of their stability regions (i.e., systems that are nearly unstable), buffer size and decoherence can have significant effects on performance metrics. We also learn that in general, increasing the buffer size from one to two qubits per link is advantageous to most systems, whereas increasing the buffer size further yields diminishing returns. The analytical results obtained in this work can serve as a useful guide toward the future design of quantum switches—e.g., by allowing the designer to determine how many quantum memories suffice for a given number of users—as well as provide valuable insight on the performance of these and similar devices.In this article, we study a quantum entanglement distribution switch that serves$k$users in a star topology. We model variants of the system as continuous-time Markov chains and obtain expressions for switch capacity, expected number of qubits stored in memory at the switch, and the quantum memory occupancy distribution. We obtain a number of analytic results for systems in which measurements are imperfect, the links are homogeneous or heterogeneous and for switches that have an infinite or finite number of quantum memories or buffers. In addition, we model the effect of decoherence of quantum states and associated cutoff times on their storage using a simple model. From numerical observations, we discover that decoherence-associated cutoff times have little effect on capacity and expected number of stored qubits for homogeneous systems. For heterogeneous systems, especially those operating near the boundaries of their stability regions (i.e., systems that are nearly unstable), buffer size and decoherence can have significant effects on performance metrics. We also learn that in general, increasing the buffer size from one to two qubits per link is advantageous to most systems, whereas increasing the buffer size further yields diminishing returns. The analytical results obtained in this work can serve as a useful guide toward the future design of quantum switches—e.g., by allowing the designer to determine how many quantum memories suffice for a given number of users—as well as provide valuable insight on the performance of these and similar devices.

IEEE Transactions on Quantum EngineeringJan 1, 202163 citations

A throughput optimal scheduling policy for a quantum switch

Thirupathaiah Vasantam, Don Towsley

We study a quantum switch that creates shared end-to-end 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 Bell-state entangled states are generated in each time-slot with certain probabilities, and the switch merges entanglements of links to create end-to-end 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 time-slot, we characterize the capacity region, which is defined as the set of arrival rates of requests for end-to-end entanglements for which there exists a scheduling policy that stabilizes the switch. We propose a Max-Weight 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.We study a quantum switch that creates shared end-to-end 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 Bell-state entangled states are generated in each time-slot with certain probabilities, and the switch merges entanglements of links to create end-to-end 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 time-slot, we characterize the capacity region, which is defined as the set of arrival rates of requests for end-to-end entanglements for which there exists a scheduling policy that stabilizes the switch. We propose a Max-Weight 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.

arXiv:2206.03205Quantum Computing, Communication, and SimulationMar 2, 202228 citations

On the Stochastic Analysis of a Quantum Entanglement Switch

Gayane Vardoyan, Saikat Guha, Philippe Nain +1 more

We study a quantum entanglement switch that serves k users in a star topology. We model variants of the system using continuous-time Markov chains (CTMCs) and obtain expressions for switch capacity and the expected number of qubits stored in memory at the switch. Using CTMCs allows us to obtain a number of analytic results for systems in which the links are homogeneous or heterogeneous and for switches that have infinite or finite buffer sizes. In addition, we can easily model the effects of decoherence of quantum states using this technique. From numerical observations, we discover that decoherence has little effect on capacity and expected number of stored qubits for homogeneous systems. For heterogeneous systems, especially those operating close to stability constraints, buffer size and decoherence can significantly affect performance. We also learn that, in general, increasing the buffer size from one to two qubits per link is advantageous to most systems, while increasing the buffer size further yields diminishing returns.We study a quantum entanglement switch that serves k users in a star topology. We model variants of the system using continuous-time Markov chains (CTMCs) and obtain expressions for switch capacity and the expected number of qubits stored in memory at the switch. Using CTMCs allows us to obtain a number of analytic results for systems in which the links are homogeneous or heterogeneous and for switches that have infinite or finite buffer sizes. In addition, we can easily model the effects of decoherence of quantum states using this technique. From numerical observations, we discover that decoherence has little effect on capacity and expected number of stored qubits for homogeneous systems. For heterogeneous systems, especially those operating close to stability constraints, buffer size and decoherence can significantly affect performance. We also learn that, in general, increasing the buffer size from one to two qubits per link is advantageous to most systems, while increasing the buffer size further yields diminishing returns.

arXiv:1903.04420ACM SIGMETRICS Performance Evaluation ReviewDec 4, 201985 citations

In this article, we study a quantum entanglement distribution switch that serves

k

users in a star topology. We model variants of the system as continuous-time Markov chains and obtain expressions for switch capacity, expected number of qubits stored in memory at the switch, and the quantum memory occupancy distribution. We obtain a number of analytic results for systems in which measurements are imperfect, the links are homogeneous or heterogeneous and for switches that have an infinite or finite number of quantum memories or buffers. In addition, we model the effect of decoherence of quantum states and associated cutoff times on their storage using a simple model. From numerical observations, we discover that decoherence-associated cutoff times have little effect on capacity and expected number of stored qubits for homogeneous systems. For heterogeneous systems, especially those operating near the boundaries of their stability regions (i.e., systems that are nearly unstable), buffer size and decoherence can have significant effects on performance metrics. We also learn that in general, increasing the buffer size from one to two qubits per link is advantageous to most systems, whereas increasing the buffer size further yields diminishing returns. The analytical results obtained in this work can serve as a useful guide toward the future design of quantum switches—e.g., by allowing the designer to determine how many quantum memories suffice for a given number of users—as well as provide valuable insight on the performance of these and similar devices.