Werner state structure and entanglement classification

TL;DR

This paper uses Lie group representation theory to analyze the structure and classification of Werner states, a special class of quantum states invariant under identical local unitary transformations, and introduces a multiqubit generalization.

Contribution

It provides a new framework for understanding Werner states through Lie group theory and introduces a multiqubit generalization of the singlet state.

Findings

Lie group methods elucidate Werner state structure

Classification of Werner states achieved via representation theory

New multiqubit singlet state generalization introduced

Abstract

We present applications of the representation theory of Lie groups to the analysis of structure and local unitary classification of Werner states, sometimes called the {\em decoherence-free} states, which are states of $n$ quantum bits left unchanged by local transformations that are the same on each particle. We introduce a multiqubit generalization of the singlet state, and a construction that assembles these into Werner states.