Average concurrence and entanglement swapping

TL;DR

This paper investigates how average concurrence, a measure of quantum entanglement, propagates through entanglement swapping in quantum networks, providing rules and bounds for qubits and qudits.

Contribution

It introduces a simple rule for average concurrence propagation in qubit entanglement swapping and explores bounds and results for mixed states and higher-dimensional systems.

Findings

Simple rule for pure qubit states

Upper bounds for mixed qubit states

Results for entanglement in qudits

Abstract

We study the role of average concurrence in entanglement swapping in quantum networks. We begin with qubit pure states, and there is a very simple rule governing the propagation of average concurrence in multiple swaps. We look at examples of mixed qubit states, and find the relation for pure states gives an upper bound on what is possible with mixed states. We then move on to qudits, where we make use of the I-concurrence. Here the situation is not as simple as for qubits, but in some cases relatively straightforward results can be obtained.