Quantifying the irreversibility of channels

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Theoretical and Mathematical Physics Pub Date : 2024-03-22 DOI:10.1134/S004057792403005X
Shunlong Luo, Yuan Sun
{"title":"Quantifying the irreversibility of channels","authors":"Shunlong Luo,&nbsp;Yuan Sun","doi":"10.1134/S004057792403005X","DOIUrl":null,"url":null,"abstract":"<p> In contrast to unitary evolutions, which are reversible, generic quantum processes (operations and quantum channels) are often irreversible. However, the degree of irreversibility is different for different channels, and it is desirable to have a quantitative characterization of irreversibility. In this paper, by exploiting the channel–state duality implemented by the Jamiołkowski–Choi isomorphism, we quantify the irreversibility of channels via entropy of the Jamiołkowski–Choi states of the corresponding channels and compare it with the notions of entanglement fidelity and entropy exchange. General properties of a reasonable measure of irreversibility are discussed from an intuitive perspective, and entropic measures of irreversibility are introduced. Several relations between irreversibility, entanglement fidelity, the degree of nonunitality, and decorrelating power are established. Some measures of irreversibility for a variety of prototypical channels are evaluated explicitly, revealing some information-theoretic aspects of the structure of channels from the perspective of irreversibility. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"218 3","pages":"426 - 451"},"PeriodicalIF":1.0000,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S004057792403005X","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0

Abstract

In contrast to unitary evolutions, which are reversible, generic quantum processes (operations and quantum channels) are often irreversible. However, the degree of irreversibility is different for different channels, and it is desirable to have a quantitative characterization of irreversibility. In this paper, by exploiting the channel–state duality implemented by the Jamiołkowski–Choi isomorphism, we quantify the irreversibility of channels via entropy of the Jamiołkowski–Choi states of the corresponding channels and compare it with the notions of entanglement fidelity and entropy exchange. General properties of a reasonable measure of irreversibility are discussed from an intuitive perspective, and entropic measures of irreversibility are introduced. Several relations between irreversibility, entanglement fidelity, the degree of nonunitality, and decorrelating power are established. Some measures of irreversibility for a variety of prototypical channels are evaluated explicitly, revealing some information-theoretic aspects of the structure of channels from the perspective of irreversibility.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
量化通道的不可逆转性
摘要 与单元演化的可逆性不同,一般量子过程(运算和量子通道)通常是不可逆的。然而,不同通道的不可逆程度是不同的,因此我们需要对不可逆性进行定量描述。本文利用贾米乌科夫斯基-乔伊同构实现的通道-状态对偶性,通过相应通道的贾米乌科夫斯基-乔伊状态的熵来量化通道的不可逆性,并将其与纠缠保真度和熵交换的概念进行比较。从直观的角度讨论了合理的不可逆度量的一般属性,并引入了不可逆的熵度量。建立了不可逆性、纠缠保真度、非单元性程度和去相关性之间的若干关系。明确评估了各种原型信道的一些不可逆度量,从不可逆的角度揭示了信道结构的一些信息论方面。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Theoretical and Mathematical Physics
Theoretical and Mathematical Physics 物理-物理:数学物理
CiteScore
1.60
自引率
20.00%
发文量
103
审稿时长
4-8 weeks
期刊介绍: Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
期刊最新文献
Hamiltonian mapping and quantum perturbation equations in the point matter black hole and noncommutative black hole models Lie group geometry: Riemann and Ricci tensors and normal forms of Lie algebras On the unique solvability of the div–curl problem in unbounded domains and energy estimates of solutions Total, classical, and quantum uncertainty matrices via operator monotone functions 3D consistency of negative flows
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1