  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.
