Parallel Self-Testing of the GHZ State with a Proof by Diagrams

TL;DR

This paper introduces the first error-tolerant parallel self-test for multiple GHZ states in a three-party setting, using diagrammatic methods from categorical quantum mechanics to verify multipartite entanglement.

Contribution

It presents a novel diagrammatic proof technique for parallel self-testing of GHZ states, extending the capability to verify multipartite states with untrusted devices.

Findings

First error-tolerant parallel self-test for GHZ states

Diagrammatic proof approach simplifies complex tensor network manipulations

Demonstrates the importance of picture-languages in quantum information

Abstract

Quantum self-testing addresses the following question: is it possible to verify the existence of a multipartite state even when one's measurement devices are completely untrusted? This problem has seen abundant activity in the last few years, particularly with the advent of parallel self-testing (i.e., testing several copies of a state at once), which has applications not only to quantum cryptography but also quantum computing. In this work we give the first error-tolerant parallel self-test in a three-party (rather than two-party) scenario, by showing that an arbitrary number of copies of the GHZ state can be self-tested. In order to handle the additional complexity of a three-party setting, we use a diagrammatic proof based on categorical quantum mechanics, rather than a typical symbolic proof. The diagrammatic approach allows for manipulations of the complicated tensor networks that arise in the proof, and gives a demonstration of the importance of picture-languages in quantum information.