{"title":"Uncertainty relations based on the \\(\\rho \\)-absolute variance for quantum channels","authors":"Cong Xu, Wen Zhou, Qing-Hua Zhang, Shao-Ming Fei","doi":"10.1007/s11128-024-04493-9","DOIUrl":null,"url":null,"abstract":"<div><p>Uncertainty principle reveals the intrinsic differences between the classical and quantum worlds, which plays a significant role in quantum information theory. By using <span>\\(\\rho \\)</span>-absolute variance, we introduce the uncertainty of quantum channels and explore its properties. By using Cauchy–Schwarz inequality and the parallelogram law, we establish the product and summation forms of the uncertainty relations for arbitrary two quantum channels, respectively. The summation form of the uncertainty inequalities based on the <span>\\(\\rho \\)</span>-absolute variance for arbitrary <i>N</i> quantum channels is also investigated, and the optimal lower bounds are presented. We illustrate our results by several typical examples.\n</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information Processing","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11128-024-04493-9","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Uncertainty principle reveals the intrinsic differences between the classical and quantum worlds, which plays a significant role in quantum information theory. By using \(\rho \)-absolute variance, we introduce the uncertainty of quantum channels and explore its properties. By using Cauchy–Schwarz inequality and the parallelogram law, we establish the product and summation forms of the uncertainty relations for arbitrary two quantum channels, respectively. The summation form of the uncertainty inequalities based on the \(\rho \)-absolute variance for arbitrary N quantum channels is also investigated, and the optimal lower bounds are presented. We illustrate our results by several typical examples.
期刊介绍:
Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.