An operator system approach to self-testing

TL;DR

This paper introduces a comprehensive operator system framework for self-testing in quantum correlations, unifying various scenarios and establishing conditions for when self-tests are also abstract self-tests.

Contribution

It develops a general operator system approach to self-testing, defining local isometries in the commuting operator model and analyzing their properties across multiple quantum scenarios.

Findings

Self-tests are always abstract self-tests in the general case.

In some cases, the converse that all abstract self-tests are actual self-tests holds.

The framework applies to correlations with quantum inputs/outputs, CHSH game, contextuality, and quantum colorings.

Abstract

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.