We develop a general framework for self-testing, in which bipartite correlations are described by states on the commuting tensor product of a pair of operator systems. We propose a definition of a local isometry between bipartite quantum systems in the commuting operator model, and define self-testing and abstract self-testing in the latter generality. We show that self-tests are in the general case always abstract self-tests and that, in some cases, the converse is also true. We apply our framework in a variety of instances, including to correlations with quantum inputs and outputs, quantum commuting correlations for the CHSH game, synchronous correlations, contextuality scenarios, quantum colourings and Schur quantum channels.
@article{arxiv.2506.17980,
title = {An operator system approach to self-testing},
author = {Jason Crann and Ivan G. Todorov and Lyudmila Turowska},
journal= {arXiv preprint arXiv:2506.17980},
year = {2025}
}