# On the Capacity Region of Bipartite and Tripartite Entanglement Switching

## TL;DR

This paper analyzes the maximum rates of bipartite and tripartite entanglement distribution in a quantum switch with a star topology, using Markov chain models to compare different switching policies and their performance.

## Contribution

It introduces analytical models for quantum entanglement switching policies, demonstrating how certain policies outperform TDM and exploring effects of decoherence and storage capacity.

## Key findings

- Best policies outperform TDM in entanglement rate
- Performance gap decreases with more users
- Decoherence has limited impact on capacity in identical-link systems

## Abstract

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 (TDM) 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.