The stabilizer dimension of graph states

TL;DR

This paper investigates the stabilizer dimension of graph states, revealing its connection to graph configurations and two-qubit correlations, thereby advancing understanding of entanglement invariants in quantum information.

Contribution

It establishes a direct link between stabilizer dimension and graph configurations as well as two-qubit correlations in graph states.

Findings

Stabilizer dimension relates to three specific graph configurations.

For n ≥ 3, stabilizer dimension equals the degree of irreducible two-qubit correlations.

Provides a new characterization of entanglement properties in graph states.

Abstract

The entanglement properties of a multiparty pure state are invariant under local unitary transformations. The stabilizer dimension of a multiparty pure state characterizes how many types of such local unitary transformations existing for the state. We find that the stabilizer dimension of an $n$-qubit ($n\ge 2$) graph state is associated with three specific configurations in its graph. We further show that the stabilizer dimension of an $n$-qubit ($n\ge 3$) graph state is equal to the degree of irreducible two-qubit correlations in the state.