Symmetric mixed states of $n$ qubits: local unitary stabilizers and entanglement classes

Abstract

We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states into six classes. These include the stabilizer types of the Werner states, the GHZ state and its generalizations, and Dicke states. For all but the zero algebra, we classify entanglement types (local unitary equivalence classes) of symmetric mixed states that have those stabilizers. We make use of the identification of symmetric density matrices with polynomials in three variables with real coefficients and apply the representation theory of SO(3) on this space of polynomials.

10 pages, 1 table, title change and minor clarifications for published version

References in corpus (7)

• Permutationally invariant quantum tomography
• The maximally entangled symmetric state in terms of the geometric measure
• Tensor Rank and Stochastic Entanglement Catalysis for Multipartite Pure States
• Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group
• Classification of nonproduct states with maximum stabilizer dimension
• Maximum stabilizer dimension for nonproduct states
• Entanglement classes of symmetric Werner states

Cited by in corpus (9)

• On the permutationally invariant part of a density matrix and nonseparability of N-qubit states
• Entanglement in highly symmetric multipartite quantum states
• Optimal quantum tomography of permutationally invariant qubits
• An alternative representation for pure symmetric states of qubits and its applications to entanglement classification
• Werner state structure and entanglement classification
• Two-qubit correlations revisited: average mutual information, relevant (and useful) observables and an application to remote state preparation
• Local unitary symmetries and entanglement invariants
• Entanglement verification using local unitary stabilizers
• Werner states from diagrams