On the Analysis of a Multipartite Entanglement Distribution Switch

TL;DR

This paper analyzes a quantum switch for distributing multipartite entanglement, deriving stability conditions, capacity, and memory usage, with implications for distributed quantum applications and queueing theory.

Contribution

It introduces a simplified model of a quantum entanglement switch with infinite memory and perfect states, providing new stability and capacity results using queueing theory techniques.

Findings

Derived necessary and sufficient stability conditions

Closed-form expressions for switch capacity

Expected number of qubits in memory

Abstract

We study a quantum switch that distributes maximally entangled multipartite states to sets of users. The entanglement switching process requires two steps: first, each user attempts to generate bipartite entanglement between itself and the switch; and second, the switch performs local operations and a measurement to create multipartite entanglement for a set of users. In this work, we study a simple variant of this system, wherein the switch has infinite memory and the links that connect the users to the switch are identical. Further, we assume that all quantum states, if generated successfully, have perfect fidelity and that decoherence is negligible. This problem formulation is of interest to several distributed quantum applications, while the technical aspects of this work result in new contributions within queueing theory. Via extensive use of Lyapunov functions, we derive necessary and sufficient conditions for the stability of the system and closed-form expressions for the switch capacity and the expected number of qubits in memory.