Lifting the maximally-entangledness assumption in robust self-testing for synchronous games
- 1Delft Institute of Applied Mathematics, TU Delft, The Netherlands
- 2QMATH, Department of Mathematical Sciences, University of Copenhagen, Denmark
Abstract
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 M I P ∗ = R E 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.
Related
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- Maximally symmetric black holes with torsion in Lovelock gravity
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- Robust self-test of the maximally entangled state of two-qubits without assuming unitary observables
- Higher-form Symmetries of Linearized Gravity in Maximally Symmetric Spaces
BibTeX
@article{vernooij2026lifting,
title = {{Lifting the maximally-entangledness assumption in robust self-testing for synchronous games}},
author = {Matthijs Vernooij and Yuming Zhao},
journal = {Quantum},
year = {2026},
month = oct,
doi = {10.22331/q-2026-10-01-2222},
url = {https://quantum-journal.org/papers/q-2026-10-01-2222/},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Lifting the maximally-entangledness assumption in robust self-testing for synchronous games
AU - Matthijs Vernooij
AU - Yuming Zhao
PY - 2026
DA - 2026/10/01
JO - Quantum
DO - 10.22331/q-2026-10-01-2222
UR - https://quantum-journal.org/papers/q-2026-10-01-2222/
AB - 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 M I P ∗ = R E 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.
SN - 2521-327X
ER -