{"paper":{"title":"The Parallel-Repeated Magic Square Game is Rigid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Anand Natarajan, Matthew Coudron","submitted_at":"2016-09-20T19:58:38Z","abstract_excerpt":"We show that the $n$-round parallel repetition of the Magic Square game of Mermin and Peres is rigid, in the sense that for any entangled strategy succeeding with probability $1 -\\varepsilon$, the players' shared state is $O(\\mathrm{poly}(n\\varepsilon))$-close to $2n$ EPR pairs under a local isometry. Furthermore, we show that, under local isometry, the players' measurements in said entangled strategy must be $O(\\mathrm{poly}(n\\varepsilon))$ close to the \"ideal\" strategy when acting on the shared state."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06306","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}