有限维量子观测是CP映射的特殊对称Dagger-Frobenius代数

Q4 Computer Science

Electronic Proceedings in Theoretical Computer Science Pub Date : 2023-11-15 DOI:10.4204/eptcs.394.21

Stefano Gogioso

{"title":"有限维量子观测是CP映射的特殊对称Dagger-Frobenius代数","authors":"Stefano Gogioso","doi":"10.4204/eptcs.394.21","DOIUrl":null,"url":null,"abstract":"We use purity, a principle borrowed from the foundations of quantum information, to show that all special symmetric $\\dagger$-Frobenius algebras in $\\operatorname{CPM}\\left(\\operatorname{fHilb}\\right)$ -- and, in particular, all classical structures -- are canonical, i.e. that they arise by doubling of special symmetric $\\dagger$-Frobenius algebras in $\\operatorname{fHilb}$. This provides an exact classification of finite-dimensional quantum observables.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"9 12","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Finite-dimensional Quantum Observables are the Special Symmetric Dagger-Frobenius Algebras of CP Maps\",\"authors\":\"Stefano Gogioso\",\"doi\":\"10.4204/eptcs.394.21\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We use purity, a principle borrowed from the foundations of quantum information, to show that all special symmetric $\\\\dagger$-Frobenius algebras in $\\\\operatorname{CPM}\\\\left(\\\\operatorname{fHilb}\\\\right)$ -- and, in particular, all classical structures -- are canonical, i.e. that they arise by doubling of special symmetric $\\\\dagger$-Frobenius algebras in $\\\\operatorname{fHilb}$. This provides an exact classification of finite-dimensional quantum observables.\",\"PeriodicalId\":30085,\"journal\":{\"name\":\"Electronic Proceedings in Theoretical Computer Science\",\"volume\":\"9 12\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Proceedings in Theoretical Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4204/eptcs.394.21\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Computer Science\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Proceedings in Theoretical Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4204/eptcs.394.21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Computer Science","Score":null,"Total":0}

引用次数: 0

摘要

我们使用纯粹性，一个从量子信息基础借用的原理，来证明$\operatorname{CPM}\左(\operatorname{fHilb}\右)$中的所有特殊对称$\dagger$-Frobenius代数，特别是所有经典结构，都是正则的，即它们是由$\operatorname{fHilb}$中的特殊对称$\dagger$-Frobenius代数的加倍产生的。这提供了有限维量子可观测物的精确分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Finite-dimensional Quantum Observables are the Special Symmetric Dagger-Frobenius Algebras of CP Maps

We use purity, a principle borrowed from the foundations of quantum information, to show that all special symmetric $\dagger$-Frobenius algebras in $\operatorname{CPM}\left(\operatorname{fHilb}\right)$ -- and, in particular, all classical structures -- are canonical, i.e. that they arise by doubling of special symmetric $\dagger$-Frobenius algebras in $\operatorname{fHilb}$. This provides an exact classification of finite-dimensional quantum observables.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊