{"title":"非多重非等维基底和不锋利的测量","authors":"Dmitry V. Dodin, I. Kovalenko","doi":"10.1117/12.801897","DOIUrl":null,"url":null,"abstract":"We consider a procedure of measurement of a quantum system in case when its dimension and the dimension of the basis of a measuring device relate as ratio of integer numbers. This procedure of measurement is introduced here as a \"procedure of measurement in different-dimensional bases\". We develop a new mathematical formalism describing this kind of measurement. It is demonstrated that when the dimension of the system is divisible by the dimension of basis for the measuring instrument, our results coincide with conventional theoretical developments. We consider measurement in different-dimensional bases as a kind of unsharp measurement.","PeriodicalId":90714,"journal":{"name":"Quantum bio-informatics V : proceedings of the quantum bio-informatics 2011, Tokyo University of Science, Japan, 7-12 March 2011. Quantum Bio-Informatics (Conference) (5th : 2011 : Tokyo, Japan)","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2008-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-multiple non-equidimensional bases and unsharp measurements\",\"authors\":\"Dmitry V. Dodin, I. Kovalenko\",\"doi\":\"10.1117/12.801897\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a procedure of measurement of a quantum system in case when its dimension and the dimension of the basis of a measuring device relate as ratio of integer numbers. This procedure of measurement is introduced here as a \\\"procedure of measurement in different-dimensional bases\\\". We develop a new mathematical formalism describing this kind of measurement. It is demonstrated that when the dimension of the system is divisible by the dimension of basis for the measuring instrument, our results coincide with conventional theoretical developments. We consider measurement in different-dimensional bases as a kind of unsharp measurement.\",\"PeriodicalId\":90714,\"journal\":{\"name\":\"Quantum bio-informatics V : proceedings of the quantum bio-informatics 2011, Tokyo University of Science, Japan, 7-12 March 2011. Quantum Bio-Informatics (Conference) (5th : 2011 : Tokyo, Japan)\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-03-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum bio-informatics V : proceedings of the quantum bio-informatics 2011, Tokyo University of Science, Japan, 7-12 March 2011. Quantum Bio-Informatics (Conference) (5th : 2011 : Tokyo, Japan)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1117/12.801897\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum bio-informatics V : proceedings of the quantum bio-informatics 2011, Tokyo University of Science, Japan, 7-12 March 2011. Quantum Bio-Informatics (Conference) (5th : 2011 : Tokyo, Japan)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1117/12.801897","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Non-multiple non-equidimensional bases and unsharp measurements
We consider a procedure of measurement of a quantum system in case when its dimension and the dimension of the basis of a measuring device relate as ratio of integer numbers. This procedure of measurement is introduced here as a "procedure of measurement in different-dimensional bases". We develop a new mathematical formalism describing this kind of measurement. It is demonstrated that when the dimension of the system is divisible by the dimension of basis for the measuring instrument, our results coincide with conventional theoretical developments. We consider measurement in different-dimensional bases as a kind of unsharp measurement.
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