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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2503.23500 |
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| _version_ | 1866913766701006848 |
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| author | Kar, Prem Nigam |
| author_facet | Kar, Prem Nigam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23500 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Self-testing for Synchronous Correlations and Games Kar, Prem Nigam Quantum Physics Computer Science and Game Theory Mathematical Physics Operator Algebras 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. |
| title | Robust Self-testing for Synchronous Correlations and Games |
| topic | Quantum Physics Computer Science and Game Theory Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2503.23500 |