Werner states from diagrams

TL;DR

This paper characterizes multiqubit Werner states by constructing a basis for Werner invariant operators and explores their entanglement properties, showing certain generalized states have separable two-qubit reductions.

Contribution

It introduces a basis for Werner invariant Hermitian operators and analyzes entanglement properties of generalized polygon diagram Werner states.

Findings

Any mixed Werner state can be uniquely expressed as a mixture of basis operators.

Generalized polygon diagram Werner states have separable two-qubit reductions.

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.