Werner states from diagrams

Abstract

We present two results on multiqubit Werner states, defined to be those states that are invariant under the collective action of any given single-qubit unitary that acts simultaneously on all the qubits. Motivated by the desire to characterize entanglement properties of Werner states, we construct a basis for the real linear vector space of Werner invariant Hermitian operators on the Hilbert space of pure states; it follows that any mixed Werner state can be written as a mixture of these basis operators with unique coefficients. Continuing a study of "polygon diagram" Werner states constructed in earlier work, with a goal to connect diagrams to entanglement properties, we consider a family of multiqubit states that generalize the singlet, and show that their 2-qubit reduced density matrices are separable.

arXiv comment18 pages, 1 figure, 2 tables, minor corrections

References in corpus (13)

• Entanglement detection
• Information Causality as a Physical Principle
• Entanglement Teleportation via Werner States
• Hiding classical data in multi-partite quantum states
• Nonadditivity of Bipartite Distillable Entanglement follows from Conjecture on Bound Entangled Werner States
• Separability properties of tripartite states with UxUxU-symmetry
• No purification for two copies of a noisy entangled state
• Positive maps and trace polynomials from the symmetric group
• Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group
• Symmetric mixed states of $n$ qubits: local unitary stabilizers and entanglement classes
• Werner state structure and entanglement classification
• A Decomposition of Separable Werner States
• Immunity of information encoded in decoherence-free subspaces to particle loss