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

Published

January 31, 2019

Author(s)

Spencer J. Breiner, Amir Kalev, Carl Miller

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 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 selftested. 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.

Proceedings Title

Proceedings of the 15th International Conference on Quantum Physics and Logic

Volume

287

Conference Dates

June 3-7, 2018

Conference Location

Halifax, CA

Conference Title

Quantum Physics and Logic

Pub Type

Conferences

Download Paper

https://doi.org/10.4204/EPTCS.287.3

Local Download

Keywords

quantum entanglement, nonlocal games, Bell inequalities, category theory

Citation

Breiner, S. , Kalev, A. and Miller, C. (2019), Parallel Self-Testing of the GHZ State with a Proof by Diagrams, Proceedings of the 15th International Conference on Quantum Physics and Logic, Halifax, CA, [online], https://doi.org/10.4204/EPTCS.287.3, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=925852 (Accessed October 9, 2025)