Generating W states with braiding operators

TL;DR

This paper demonstrates how braiding operators and algebraic structures can generate W states in multi-qubit systems, extending the topological-entanglement correspondence beyond Bell and GHZ states.

Contribution

It introduces new methods using extraspecial 2-group generators and partition algebras to produce W states, and presents a generalized Yang-Baxter operator for embedding W states.

Findings

W states generated in four-qubit space using extraspecial 2-groups

W states generated in three-qubit space using partition algebras

A unitary generalized Yang-Baxter operator embeds W$_n$ states in $(2n-1)$-qubit space

Abstract

Braiding operators can be used to create entangled states out of product states, thus establishing a correspondence between topological and quantum entanglement. This is well-known for maximally entangled Bell and GHZ states and their equivalent states under Stochastic Local Operations and Classical Communication, but so far a similar result for W states was missing. Here we use generators of extraspecial 2-groups to obtain the W state in a four-qubit space and partition algebras to generate the W state in a three-qubit space. We also present a unitary generalized Yang-Baxter operator that embeds the W$_n$ state in a $(2n-1)$-qubit space.