A Note on the Entropy of Entanglement and Entanglement Swapping Bounds

TL;DR

This paper presents elementary methods to analyze the evolution of correlations in multipartite quantum systems, establishing bounds on entanglement transfer during swapping processes and showing correlation monotonicity under certain interactions.

Contribution

It introduces a simple approach to derive bounds on correlation and entanglement evolution in multipartite quantum systems, including entanglement swapping scenarios.

Findings

Total correlation in bipartite systems cannot decrease under unitary interactions.

In 4-qubit entanglement swapping, transferred entanglement is bounded by the minimum initial entanglements.

Elementary methods suffice to derive general bounds on correlation dynamics.

Abstract

Using the information content of correlations between multipartite systems, together with the notion of partitioning, we show that some general results about the evolution of correlations in quantum systems can be derived with only elementary methods. In particular, we show that for 2 quantum systems A and B, each comprised of a number of sub-systems, in which a partition of A interacts unitarily with a partition of B, then the total correlation can only increase (or remain unchanged) and is given simply by the sum of the initial correlation and the correlation that develops as a result of the interaction. We then show that in a 4 qubit entanglement swapping process the transferred degree of entanglement is bounded by the lower of the initial degrees of entanglements of the qubits.