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

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.

4 pages, 3 figures. Version 2 has numerous small changes and corrections

References in corpus (4)

• On maximal entanglement between two pairs in four-qubit pure states
• Classification of nonproduct states with maximum stabilizer dimension
• Maximum stabilizer dimension for nonproduct states
• Minimum orbit dimension for local unitary action on n-qubit pure states