On the Stochastic Analysis of a Quantum Entanglement Distribution Switch

• Published in: IEEE transactions on quantum engineering Vol. 2; pp. 1 - 16
• Main Authors: Vardoyan, Gayane, Guha, Saikat, Nain, Philippe, Towsley, Don
• Format: Journal Article
• Language: English
• Published: New York IEEE 2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Analytical models; Buffers; Computer architecture; Computer Science; Continuous time systems; Markov chains; Networking and Internet Architecture; Numerical models; Occupancy; Performance measurement; Quantum entanglement; Quantum mechanics; Quantum phenomena; Quantum repeaters; Qubit; Qubits (quantum computing); remote entanglement generation; Repeaters; Switches; Topology
• ISSN: 2689-1808; 2689-1808
• DOI: 10.1109/TQE.2021.3058058

In this article, we study a quantum entanglement distribution switch that serves <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula> 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.