Continuous variable graph states: entanglement and graph properties

TL;DR

This paper introduces a geometric measure of entanglement for continuous variable states and explores how the entanglement in graph states of harmonic oscillators relates to vertex degree.

Contribution

It defines a new entanglement measure for continuous variables and links entanglement in graph states to graph properties like vertex degree.

Findings

Entanglement is determined by vertex degree in graph states.

The geometric measure applies to states generated by unitary operations on harmonic oscillators.

Provides insights into entanglement structure in continuous variable quantum systems.

Abstract

We propose the definition of the geometric measure of entanglement for continuous variable states. On the basis of this definition we examine entanglement of the graph states obtained as a result of action of a unitary operator on the ground state of a system of $N$ noninteracting harmonic oscillators. We find that the entanglement of a harmonic oscillator with other ones is defined by the value of its vertex degree.