Entanglement distribution in pure non-Gaussian tripartite states: a Schmidt decomposition approach

TL;DR

This paper investigates how entanglement is distributed among three coupled quantum harmonic oscillators using Schmidt decomposition, revealing insights into multipartite entanglement sharing and its implications for quantum information processing.

Contribution

It introduces a Schmidt decomposition-based method to analyze entanglement distribution in pure non-Gaussian tripartite states of coupled oscillators, advancing understanding of multipartite entanglement.

Findings

Schmidt coefficients evolve with interaction strengths

Entanglement sharing patterns depend on coupling parameters

Insights into multipartite entanglement structure

Abstract

We study entanglement in a system of three coupled quantum harmonic oscillators. Specifically, we use the Schmidt decomposition to analyze how the entanglement is distributed among the three subsystems. The Schmidt decomposition is a powerful mathematical tool for characterizing bipartite entanglement in composite quantum systems. It allows to write a multipartite quantum state as a sum of product states between the subsystems, with coefficients known as Schmidt coefficients. We apply this decomposition to the general quantum state of three coupled oscillators and study how the Schmidt coefficients evolve as the interaction strengths between the oscillators are varied. This provides insight into how entanglement is shared between the different bipartitions of the overall three-particle system. Our results advance the fundamental understanding of multipartite entanglement in networked quantum systems. They also have implications for quantum information processing using multiple entangled nodes.