{"title":"两人纠缠博弈是np困难的","authors":"Anand Natarajan, Thomas Vidick","doi":"10.4230/LIPIcs.CCC.2018.20","DOIUrl":null,"url":null,"abstract":"We show that the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length is NP-hard to approximate to within constant factors. As a corollary, the inclusion $\\mathrm{NEXP}\\subseteq\\mathrm{MIP}^*$, first shown in [IV12] with three provers, holds with two provers only. The proof is based on a simpler, improved analysis of the low-degree test Raz and Safra (STOC'97) against two entangled provers.","PeriodicalId":246506,"journal":{"name":"Cybersecurity and Cyberforensics Conference","volume":"36 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":"{\"title\":\"Two-player entangled games are NP-hard\",\"authors\":\"Anand Natarajan, Thomas Vidick\",\"doi\":\"10.4230/LIPIcs.CCC.2018.20\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length is NP-hard to approximate to within constant factors. As a corollary, the inclusion $\\\\mathrm{NEXP}\\\\subseteq\\\\mathrm{MIP}^*$, first shown in [IV12] with three provers, holds with two provers only. The proof is based on a simpler, improved analysis of the low-degree test Raz and Safra (STOC'97) against two entangled provers.\",\"PeriodicalId\":246506,\"journal\":{\"name\":\"Cybersecurity and Cyberforensics Conference\",\"volume\":\"36 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-10-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cybersecurity and Cyberforensics Conference\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.CCC.2018.20\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cybersecurity and Cyberforensics Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.CCC.2018.20","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We show that the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length is NP-hard to approximate to within constant factors. As a corollary, the inclusion $\mathrm{NEXP}\subseteq\mathrm{MIP}^*$, first shown in [IV12] with three provers, holds with two provers only. The proof is based on a simpler, improved analysis of the low-degree test Raz and Safra (STOC'97) against two entangled provers.
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