Local unitary classes of states invariant under permutation subgroups

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.

arXiv comment(there are no changes in the article from version 3 to version 4, only corrections to typos in the comments field) Corrected comments: version 3 has two corrected citations and some minor edits, 14 pages, 5 figures

References in corpus (12)

• Global entanglement in multiparticle systems
• Permutationally invariant quantum tomography
• How entangled can two couples get?
• Operational Families of Entanglement Classes for Symmetric $N$-Qubit States
• The maximally entangled symmetric state in terms of the geometric measure
• Entanglement and symmetry in permutation symmetric states
• Multipartite entanglement verification resistant against dishonest parties
• Local unitary symmetries of hypergraph states
• Entanglement in highly symmetric multipartite quantum states
• Operational Entanglement Families of Symmetric Mixed N-Qubit States
• Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group
• Classification of nonproduct states with maximum stabilizer dimension