Robust self-testing for linear constraint system games

Understand

We study linear constraint system (LCS) games over the ring of arithmetic modulo $d$.

• We give a new proof that certain LCS games (the Mermin--Peres Magic Square and Magic Pentagram over binary alphabets, together with parallel repetitions of these) have unique winning strategies, where the uniqueness is robust to small perturbations.
• In order to prove our result, we extend the representation-theoretic framework of Cleve, Liu, and Slofstra (Journal of Mathematical Physics 58.1 (2017): 012202.) to apply to linear constraint games over $\mathbb{Z}_d$ for $d\geq 2$.
• We package our main argument into machinery which applies to any nonabelian finite group with a ''solution group'' presentation.