Lifting the maximally-entangledness assumption in robust self-testing for synchronous games

Fuente: arXiv
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Main Authors: Vernooij, Matthijs, Zhao, Yuming
Format: Preprint
Published: 2025
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author Vernooij, Matthijs
Zhao, Yuming
author_facet Vernooij, Matthijs
Zhao, Yuming
contents Robust self-testing in non-local games allows a classical referee to certify that two untrustworthy players are able to perform a specific quantum strategy up to high precision. Proving robust self-testing results becomes significantly easier when one restricts the allowed strategies to symmetric projective maximally entangled (PME) strategies, which allow natural descriptions in terms of tracial von Neumann algebras. This has been exploited in the celebrated MIP*=RE paper and related articles to prove robust self-testing results for synchronous games when restricting to PME strategies. However, the PME assumptions are not physical, so these results need to be upgraded to make them physically relevant. In this work, we do just that: we prove that any perfect synchronous game which is a robust self-test when restricted to PME strategies, is in fact a robust self-test for all strategies. We then apply our result to the Quantum Low Degree Test to find an efficient $n$-qubit test.
format Preprint
id arxiv_https___arxiv_org_abs_2505_05994
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Lifting the maximally-entangledness assumption in robust self-testing for synchronous games
Vernooij, Matthijs
Zhao, Yuming
Quantum Physics
Operator Algebras
81P40, 46L60
Robust self-testing in non-local games allows a classical referee to certify that two untrustworthy players are able to perform a specific quantum strategy up to high precision. Proving robust self-testing results becomes significantly easier when one restricts the allowed strategies to symmetric projective maximally entangled (PME) strategies, which allow natural descriptions in terms of tracial von Neumann algebras. This has been exploited in the celebrated MIP*=RE paper and related articles to prove robust self-testing results for synchronous games when restricting to PME strategies. However, the PME assumptions are not physical, so these results need to be upgraded to make them physically relevant. In this work, we do just that: we prove that any perfect synchronous game which is a robust self-test when restricted to PME strategies, is in fact a robust self-test for all strategies. We then apply our result to the Quantum Low Degree Test to find an efficient $n$-qubit test.
title Lifting the maximally-entangledness assumption in robust self-testing for synchronous games
topic Quantum Physics
Operator Algebras
81P40, 46L60
url https://arxiv.org/abs/2505.05994