A quantum switch is one of the most fundamental network elements for connecting different quantum devices. In this paper, we explore the “optimal entanglement policy” of a quantum switch under a scenario where the stored and entangled qubits in the quantum switch may undergo a decoherence process. Finding an optimal entanglement policy is important as it enables a quantum switch to make a judicious basis measurement based on the number of existing link-level entanglements to maximize the “weighted throughput”. We use a Markov decision process framework to model the dynamics of the quantum switch, and theoretically reveal a threshold-based relationship between bipartite and tripartite policies under a very general class of weight functions with a weight parameter β. We further extend our analysis to uncover athreshold-based structure of optimal policies. In particular, the optimal policy for the quantum switch is a bipartite or tripartite policy when β is below a threshold β∗Bor above a threshold β∗T, respectively. When β∗B∗T, the optimal policy becomes a “threshold-based and state-dependent entanglement policy”. We also extend the work to allow a mixture of bipartite and tripartite policies by introducing a state-dependent mixed action. We theoretically show threshold-related relationships between mixed and bipartite/tripartite policies. Moreover, we extend this analysis to study optimal policies and characterize the threshold-based structure when the mixed action is considered. We carry out extensive numerical experiments to confirm that the optimal entanglement policy has such structural property when the mixed action is considered or not.
A quantum switch is one of the most fundamental network elements for connecting different quantum devices. In this paper, we explore the “optimal entanglement policy” of a quantum switch under a scenario where the stored and entangled qubits in the quantum switch may undergo a decoherence process. Finding an optimal entanglement policy is important as it enables a quantum switch to make a judicious basis measurement based on the number of existing link-level entanglements to maximize the “weighted throughput”. We use a Markov decision process framework to model the dynamics of the quantum switch, and theoretically reveal a threshold-based relationship between bipartite and tripartite policies under a very general class of weight functions with a weight parameter β. We further extend our analysis to uncover athreshold-based structure of optimal policies. In particular, the optimal policy for the quantum switch is a bipartite or tripartite policy when β is below a threshold β∗Bor above a threshold β∗T, respectively. When β∗B∗T, the optimal policy becomes a “threshold-based and state-dependent entanglement policy”. We also extend the work to allow a mixture of bipartite and tripartite policies by introducing a state-dependent mixed action. We theoretically show threshold-related relationships between mixed and bipartite/tripartite policies. Moreover, we extend this analysis to study optimal policies and characterize the threshold-based structure when the mixed action is considered. We carry out extensive numerical experiments to confirm that the optimal entanglement policy has such structural property when the mixed action is considered or not.
The quantum switch is a vital component for the development of the quantum internet. In an entanglement distribution network, the function of a quantum switch is to generate elementary entanglement with its clients followed by entanglement swapping to distribute end-to-end entanglement of sufficiently high fidelity between clients. The threshold on entanglement fidelity is any quality of service requirement specified by the clients as dictated by the application they run on the network. We consider a discrete time model for a quantum switch that attempts generation of fresh elementary entanglement with clients in each time step in the form of maximally entangled qubit pairs, or Bell pairs, which succeed probabilistically; the successfully generated Bell pairs are stored in noisy quantum memories until they can be swapped. We focus on establishing the value of entanglement distillation of the stored Bell pairs prior to entanglement swapping in presence of their inevitable aging, i.e., decoherence: For a simple instance of a switch with two clients, an exponential decay of entanglement fidelity, and a wellknown probabilistic but heralded two-to-one distillation protocol, given a threshold end-to-end entanglement fidelity, we use the Markov Decision Processes framework to identify the optimal action policy - to wait, to distill, or to swap that maximizes throughput. We compare the switch's performance under the optimal distillation-enabled policy with that excluding distillation. Simulations of the two policies demonstrate the improvements that are possible in principle via optimal use of distillation with respect to average throughput, average fidelity and jitter of end-to-end entanglement, as functions of fidelity threshold. Our model thus helps capture the role of entanglement distillation in mitigating the effects of decoherence in a quantum switch in an entanglement distribution network, adding to the growing literature on quantum switches.
With a growing number of quantum networks in operation, there is a pressing need for performance analysis of quantum switching technologies. A quantum switch establishes, distributes, and maintains entanglements across a network. In contrast to a classical switching fabric, a quantum switch is a two-sided queueing network. The switch generates Link-Level Entanglements (LLEs) across links that connect users to the switch, which are then fused to process the network's entanglement requests. First, we characterize the capacity region that is defined as the set of entanglement request rates for which there exists a scheduling policy stabilizing the system. We then show that a sequence of Max-Weight policies that we propose achieve throughput optimality in the asymptotic sense. Our proof techniques analyse a two-time scale separation phenomenon at the fluid scale for a general switch topology. This allows us to demonstrate that the optimal fluid dynamics are given by a scheduling algorithm that solves a certain average reward Markov Decision Process.
With a growing number of quantum networks in operation, there is a pressing need for performance analysis of quantum switching technologies. A quantum switch establishes, distributes, and maintains entanglements across a network. In contrast to a classical switching fabric, a quantum switch is a two-sided queueing network. The switch generates Link-Level Entanglements (LLEs) across links that connect users to the switch, which are then fused to process the network's entanglement requests. First, we characterize the capacity region that is defined as the set of entanglement request rates for which there exists a scheduling policy stabilizing the system. We then show that a sequence of Max-Weight policies that we propose achieve throughput optimality in the asymptotic sense. Our proof techniques analyse a two-time scale separation phenomenon at the fluid scale for a general switch topology. This allows us to demonstrate that the optimal fluid dynamics are given by a scheduling algorithm that solves a certain average reward Markov Decision Process.
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 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 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.