{"title":"GHZ游戏的平行重复:指数衰减","authors":"M. Braverman, Subhash Khot, Dor Minzer","doi":"10.48550/arXiv.2211.13741","DOIUrl":null,"url":null,"abstract":"We show that the value of the $n$-fold repeated GHZ game is at most $2^{-\\Omega(n)}$, improving upon the polynomial bound established by Holmgren and Raz. Our result is established via a reduction to approximate subgroup type questions from additive combinatorics.","PeriodicalId":11639,"journal":{"name":"Electron. Colloquium Comput. Complex.","volume":"471 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Parallel Repetition for the GHZ Game: Exponential Decay\",\"authors\":\"M. Braverman, Subhash Khot, Dor Minzer\",\"doi\":\"10.48550/arXiv.2211.13741\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the value of the $n$-fold repeated GHZ game is at most $2^{-\\\\Omega(n)}$, improving upon the polynomial bound established by Holmgren and Raz. Our result is established via a reduction to approximate subgroup type questions from additive combinatorics.\",\"PeriodicalId\":11639,\"journal\":{\"name\":\"Electron. Colloquium Comput. Complex.\",\"volume\":\"471 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electron. Colloquium Comput. Complex.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2211.13741\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electron. Colloquium Comput. Complex.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2211.13741","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Parallel Repetition for the GHZ Game: Exponential Decay
We show that the value of the $n$-fold repeated GHZ game is at most $2^{-\Omega(n)}$, improving upon the polynomial bound established by Holmgren and Raz. Our result is established via a reduction to approximate subgroup type questions from additive combinatorics.
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