{"title":"量子t型设计:量子世界中的t型独立","authors":"A. Ambainis, J. Emerson","doi":"10.1109/CCC.2007.26","DOIUrl":null,"url":null,"abstract":"A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate quantum t-designs for arbitrary t. We then show that an approximate 4-design provides a derandomization of the statedistinction problem considered by Sen (quant-ph/0512085), which is relevant to solving certain instances of the hidden subgroup problem.","PeriodicalId":175854,"journal":{"name":"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)","volume":"196 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"164","resultStr":"{\"title\":\"Quantum t-designs: t-wise Independence in the Quantum World\",\"authors\":\"A. Ambainis, J. Emerson\",\"doi\":\"10.1109/CCC.2007.26\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate quantum t-designs for arbitrary t. We then show that an approximate 4-design provides a derandomization of the statedistinction problem considered by Sen (quant-ph/0512085), which is relevant to solving certain instances of the hidden subgroup problem.\",\"PeriodicalId\":175854,\"journal\":{\"name\":\"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)\",\"volume\":\"196 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-01-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"164\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CCC.2007.26\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CCC.2007.26","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Quantum t-designs: t-wise Independence in the Quantum World
A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate quantum t-designs for arbitrary t. We then show that an approximate 4-design provides a derandomization of the statedistinction problem considered by Sen (quant-ph/0512085), which is relevant to solving certain instances of the hidden subgroup problem.
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