Local unitary classes of states invariant under permutation subgroups

TL;DR

This paper explores the classification and entanglement properties of multi-qubit states invariant under permutation subgroups, extending symmetrization and state representations to new subgroup classes.

Contribution

It generalizes symmetrization, Dicke states, and Majorana representation to permutation subgroups like alternating, cyclic, and dihedral groups, providing new insights into invariant state classes.

Findings

Characterization of states invariant under specific permutation subgroups

Analysis of entanglement properties of these states

Extension of state representations to new subgroup classes

Abstract

The study of entanglement properties of multi-qubit states that are invariant under permutations of qubits is motivated by potential applications in quantum computing, quantum communication, and quantum metrology. In this work, we generalize the notions of symmetrization, Dicke states, and the Majorana representation to the alternating, cyclic, and dihedral subgroups of the full group of permutations. We use these tools to characterize states that are invariant under these subgroups and analyze their entanglement properties.