Entanglement Distribution in a Quantum Network, a Multi-Commodity Flow-Based Approach

TL;DR

This paper presents a polynomial-time linear programming approach to optimize entanglement distribution rates in quantum networks, considering fidelity constraints and practical generation protocols.

Contribution

It introduces a novel linear programming formulation and an efficient path selection algorithm for maximizing entanglement distribution in quantum networks.

Findings

Maximized entanglement distribution rate under fidelity constraints.

Polynomial-time algorithms for optimization and path selection.

Practical protocol for achieving the computed rates.

Abstract

We consider the problem of optimising the achievable EPR-pair distribution rate between multiple source-destination pairs in a quantum internet, where the repeaters may perform a probabilistic bell-state measurement and we may impose a minimum end-to-end fidelity as a requirement. We construct an efficient linear programming formulation that computes the maximum total achievable entanglement distribution rate, satisfying the end-to-end fidelity constraint in polynomial time (in the number of nodes in the network). We also propose an efficient algorithm that takes the output of the linear programming solver as an input and runs in polynomial time (in the number of nodes) to produce the set of paths to be used to achieve the entanglement distribution rate. Moreover, we point out a practical entanglement generation protocol which can achieve those rates.