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On the Stochastic Analysis of a Quantum Entanglement Distribution Switch

Gayane Vardoyan 1 Saikat Guha 2 Philippe Nain 3 Don Towsley 1
3 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme, IXXI - Institut Rhône-Alpin des systèmes complexes
Abstract : 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 (CTMCs) 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, while 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.
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Submitted on : Saturday, March 20, 2021 - 7:51:33 PM
Last modification on : Tuesday, May 17, 2022 - 2:34:26 PM
Long-term archiving on: : Monday, June 21, 2021 - 6:19:10 PM

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Gayane Vardoyan, Saikat Guha, Philippe Nain, Don Towsley. On the Stochastic Analysis of a Quantum Entanglement Distribution Switch. IEEE Transactions on Quantum Engineering, IEEE, 2021, ⟨10.1109/TQE.2021.3058058⟩. ⟨hal-03175703⟩

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