  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.
