Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states

TL;DR

This paper introduces efficient numerical techniques for constructing entanglement witnesses near symmetric states, enabling practical detection of genuine multi-qubit entanglement with minimal measurement effort.

Contribution

It provides novel numerical methods for designing entanglement witnesses that are efficient and tailored for symmetric states, including local decomposition strategies.

Findings

Successfully detected entanglement near a six-qubit Dicke state

Developed measurement-efficient witness operators

Provided methods for local decomposition of symmetric operators

Abstract

We present general numerical methods to construct witness operators for entanglement detection and estimation of the fidelity. Our methods are applied to detecting entanglement in the vicinity of a six-qubit Dicke state with three excitations and also to further entangled symmetric states. All our witnesses are designed to keep the measurement effort small. We present also general results on the efficient local decomposition of permutationally invariant operators, which makes it possible to measure projectors to symmetric states efficiently