Distribution of entanglement in networks of bi-partite full-rank mixed states

TL;DR

This paper investigates methods to optimize entanglement distribution in quantum networks with mixed states, demonstrating improved protocols over simple shortest-path strategies and analyzing their performance in Erdős–Rényi networks.

Contribution

It introduces optimized entanglement swapping and purification protocols with parametrized choices, enhancing entanglement distribution efficiency in quantum networks.

Findings

Optimized protocols outperform simple shortest-chain methods.

Average entanglement gain calculated at the critical point in Erdős–Rényi networks.

Protocols depend strongly on the chosen measure of improvement.

Abstract

We study quantum entanglement distribution on networks with full-rank bi-partite mixed states linking qubits on nodes. In particular, we use entanglement swapping and purification to partially entangle widely separated nodes. The simplest method consists of performing entanglement swappings along the shortest chain of links connecting the two nodes. However, we show that this method may be improved upon by choosing a protocol with a specific ordering of swappings and purifications. A priori, the design that produces optimal improvement is not clear. However, we parametrize the choices and find that the optimal values depend strongly on the desired measure of improvement. As an initial application, we apply the new improved protocols to the Erd\"os--R\'enyi network and obtain results including low density limits and an exact calculation of the average entanglement gained at the critical point.