Ground State Entanglement in a Combination of Star And Ring Geometries Of Interacting Spins

TL;DR

This paper investigates how combining star and ring spin networks can optimize ground state entanglement, revealing complex behaviors and potential for generating robust multi-particle entangled states.

Contribution

It introduces a weighted combination of star and ring geometries to optimize ground state entanglement and provides exact and intuitive explanations for observed behaviors.

Findings

Weighted combinations can maximize entanglement in certain configurations

Ground state entanglement exhibits jumps and counterintuitive patterns

A four-qubit GHZ state can be generated from the ground state

Abstract

We compare a star and a ring network of interacting spins in terms of the entanglement they can provide between the nearest and the next to nearest neighbor spins in the ground state. We then investigate whether this entanglement can be optimized by allowing the system to interact through a weighted combination of the star and the ring geometries. We find that such a weighted combination is indeed optimal in certain circumstances for providing the highest entanglement between two chosen spins. The entanglement shows jumps and counterintuitive behavior as the relative weighting of the star and the ring interactions is varied. We give an exact mathematical explanation of the behavior for a five qubit system (four spins in a ring and a central spin) and an intuitive explanation for larger systems. For the case of four spins in a ring plus a central spin, we demonstrate how a four qubit GHZ state can be generated as a simple derivative of the ground state. Our calculations also demonstrate that some of the multi-particle entangled states derivable from the ground state of a star network are sufficiently robust to the presence of nearest neighbor ring interactions.