Entangled symmetric states and copositive matrices

TL;DR

This paper explores the relationship between entanglement in symmetric quantum states and copositive matrices, introducing new bound entangled states and entanglement witnesses in odd dimensions.

Contribution

It extends the correspondence between copositive matrices and entanglement witnesses to symmetric states beyond diagonal symmetric states, revealing new bound entangled states.

Findings

Constructed entanglement witnesses from extended copositive matrices.

Provided new examples of bound entangled symmetric states in odd dimensions.

Extended the theoretical framework linking copositive matrices and quantum entanglement.

Abstract

Entanglement in symmetric quantum states and the theory of copositive matrices are intimately related concepts. For the simplest symmetric states, i.e., the diagonal symmetric (DS) states, it has been shown that there exists a correspondence between exceptional (non-exceptional) copositive matrices and non-decomposable (decomposable) Entanglement Witnesses (EWs). Here we show that EWs of symmetric, but not DS, states can also be constructed from extended copositive matrices, providing new examples of bound entangled symmetric states, together with their corresponding EWs, in arbitrary odd dimensions.