General conditions for the generation of long-distance entanglement

TL;DR

This paper establishes necessary conditions for generating long-distance entanglement in quantum systems, emphasizing the roles of mediator system properties and external fields, with examples showing how external fields can enhance entanglement.

Contribution

It provides new theoretical conditions for long-distance entanglement generation, including the necessity of non-classical mediator interactions and external fields, and demonstrates enhancement via external fields on the mediator.

Findings

Long-distance entanglement cannot be generated if the mediator interaction is classical.

External fields on adjacent spins are necessary alongside fields on probe spins.

External fields on the mediator can significantly enhance entanglement.

Abstract

We generally investigate necessary conditions for the generation of the long-distance entanglement. We consider a quantum system in which a system mediates the indirect interaction between two spins, which we refer to as probe spins. First, we weaken the coupling between each probe spin and the mediator system to the infinitesimal strength in order to generate the long-distance entanglement. We give two necessary conditions for the mediator system to generate the long-distance entanglement. We prove that the indirect interaction cannot generate the entanglement if it is `classical.' We also give a necessary condition for the effective fields on the probe spins to satisfy. Second, we generate the long-distance entanglement by the use of only external fields. We show that external fields on the adjacent spins to the probes are necessary in addition to external fields on the probe spins. Finally, we consider the cases where the coupling strength between each probe spin and the mediator system is finite. In particular, we show two examples where the external fields on the mediator system highly enhance the long-distance entanglement.