Relay entanglement and clusters of correlated spins

TL;DR

This paper introduces the concept of relay entanglement in spin chains, analyzing how entanglement propagates and forms clusters, with implications for understanding quantum correlations and their dynamics.

Contribution

It proposes the relay entanglement measure and studies entangled cluster formation, providing new insights into the dynamics of quantum correlations in spin chains.

Findings

Relay entanglement sums all pairwise entanglements in the chain.

Remote pairwise entanglements are analyzed using partial sums.

Cluster lifetime decreases as cluster size increases.

Abstract

Considering a spin-1/2 chain, we {suppose} that the entanglement passes from a given pair of particles to another one, thus establishing the relay transfer of entanglement along the chain. Therefore, we introduce the relay entanglement as a sum of all pairwise entanglements in a spin chain. For more detailed studying the effects of {remote} pairwise entanglements, we use the partial sums collecting entanglements between the spins separated by up to a certain number of nodes. The problem of entangled cluster formation is considered, and the geometric mean entanglement is introduced as a {characteristics} of quantum correlations in a cluster. Generally, the life-time of a cluster decreases with an increase in its size.