Constant-sized robust self-tests for states and measurements of unbounded dimension

Understand

We consider correlations, $p_{n,x}$, arising from measuring a maximally entangled state using $n$ measurements with two outcomes each, constructed from $n$ projections that add up to $xI$.

• We show that the correlations $p_{n,x}$ robustly self-test the underlying states and measurements.
• To achieve this, we lift the group-theoretic Gowers-Hatami based approach for proving robust self-tests to a more natural algebraic framework.
• A key step is to obtain an analogue of the Gowers-Hatami theorem allowing to perturb an "approximate" representation of the relevant algebra to an exact one.