Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group

TL;DR

This paper classifies n-qubit quantum states stabilized by the diagonal subgroup of local unitaries, providing a basis and criteria for stabilizer size, advancing understanding of entanglement classification.

Contribution

It introduces a basis for these states parameterized by chord diagrams and criteria for stabilizer size, aiding entanglement classification.

Findings

Basis parameterized by nonintersecting chord diagrams

Criterion for stabilizer being exactly the diagonal subgroup

Part of a larger program to classify entanglement types

Abstract

We classify, up to local unitary equivalence, the set of $n$-qubit states that is stabilized by the diagonal subgroup of the local unitary group. We exhibit a basis for this set, parameterized by diagrams of nonintersecting chords connecting pairs of points on a circle, and give a criterion for when the stabilizer is precisely the diagonal subgroup and not larger. This investigation is part of a larger program to partially classify entanglement type (local unitary equivalence class) via analysis of stabilizer structure.