Robust self testing of the 3-qubit $W$ state

TL;DR

This paper develops a robust, device-independent method for self-testing the three-qubit $W$ state, extending previous bipartite and graph state approaches, with bounds resilient to experimental errors.

Contribution

It introduces a novel self-testing protocol for the three-qubit $W$ state and demonstrates its robustness against experimental imperfections.

Findings

Successfully self-tests the three-qubit $W$ state

Extends self-testing methods to other pure three-qubit states

Provides bounds that are robust to experimental errors

Abstract

Self-testing is a device independent method which can be used to determine the nature of a physical system or device, without knowing any detail of the inner mechanism or the physical dimension of Hilbert space of the system. The only information required are the number of measurements, number of outputs of each measurement and the statistics of each measurement. Earlier works on self testing restricted either to two parties scenario or multipartite graph states. Here, we construct a method to self-test the three-qubit $W$ state, and show how to extend it to other pure three-qubit states. Our bounds are robust against the inevitable experimental errors.