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 (9)

• How entangled can two couples get?
• On multi-particle entanglement
• Local symmetry properties of pure 3-qubit states
• Quantum Black Holes: Entropy and Entanglement on the Horizon
• 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
• Classification of n-qubit states with minimum orbit dimension

Cited by in corpus (10)

• Local Unitary Classification of Arbitrary Dimensional Multipartite Pure States
• Symmetric mixed states of $n$ qubits: local unitary stabilizers and entanglement classes
• Werner state structure and entanglement classification
• Local unitary classes of states invariant under permutation subgroups
• The stabilizer dimension of graph states
• Immunity of information encoded in decoherence-free subspaces to particle loss
• Entanglement classes of symmetric Werner states
• Local unitary group stabilizers and entanglement for multiqubit symmetric states
• Entanglement verification using local unitary stabilizers
• Werner states from diagrams