{"title":"Second quantised information distance","authors":"Songsong Dai","doi":"10.1049/qtc2.12050","DOIUrl":null,"url":null,"abstract":"<p>The Kolmogorov complexity of a string is the minimum length of a programme that can produce that string. Information distance between two strings based on Kolmogorov complexity is defined as the minimum length of a programme that can transform either string into the other one, both ways. The second quantised Kolmogorov complexity of a quantum state is the minimum average length of a quantum programme that can reproduce that state. In this paper, a second quantised information distance is defined based on the second quantised Kolmogorov complexity. It is described as the minimum average length of a transformation quantum programme between two quantum states. This distance's basic properties are discussed. A practical analogue of quantum information distance is also developed based on quantum data compression.</p>","PeriodicalId":100651,"journal":{"name":"IET Quantum Communication","volume":"4 1","pages":"17-24"},"PeriodicalIF":2.5000,"publicationDate":"2022-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/qtc2.12050","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IET Quantum Communication","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1049/qtc2.12050","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"QUANTUM SCIENCE & TECHNOLOGY","Score":null,"Total":0}
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Abstract
The Kolmogorov complexity of a string is the minimum length of a programme that can produce that string. Information distance between two strings based on Kolmogorov complexity is defined as the minimum length of a programme that can transform either string into the other one, both ways. The second quantised Kolmogorov complexity of a quantum state is the minimum average length of a quantum programme that can reproduce that state. In this paper, a second quantised information distance is defined based on the second quantised Kolmogorov complexity. It is described as the minimum average length of a transformation quantum programme between two quantum states. This distance's basic properties are discussed. A practical analogue of quantum information distance is also developed based on quantum data compression.
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