Robust Self-testing for Synchronous Correlations and Games

Prem Nigam Kar

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arXiv · 2503.23500

Robust Self-testing for Synchronous Correlations and Games

Prem Nigam Kar

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Abstract

We develop an abstract operator-algebraic characterization of robust self-testing for synchronous correlations and games. Specifically, we show that a synchronous correlation is a robust self-test if and only if there is a unique state on an appropriate $C^*$-algebra that "implements" the correlation. Extending this result, we prove that a synchronous game is a robust self-test if and only if its associated $C^*$-algebra admits a unique amenable tracial state. This framework allows us to establish that all synchronous correlations and games that serve as commuting operator self-tests for finite-dimensional strategies are also robust self-tests. As an application, we recover sufficient conditions for linear constraint system games to exhibit robust self-testing. We also demonstrate the existence of a synchronous nonlocal game that is a robust self-test but not a commuting operator self-test, showing that these notions are not equivalent.

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Prem Nigam Kar. 2025-03-30. Robust Self-testing for Synchronous Correlations and Games. https://arxiv.org/abs/2503.23500

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