{"title":"Quantum coherence and weak values based on rank-1 POVMs","authors":"Ouyang Yu, Zhengli Chen, Fangguo Ren, Feier Han","doi":"10.1007/s11128-025-04685-x","DOIUrl":null,"url":null,"abstract":"<div><p>In this article, we first obtain a characterization of relationships between pairwise linearly independent (PLI) rank-1 POVMs and Hamel bases for <span>\\({\\mathbb {C}}^{d}\\)</span>. By utilizing the obtained relationships, a necessary and sufficient condition is provided for the set of incoherent states based on PLI rank-1 POVM to be empty. Secondly, we deduce a detailed characterization of incoherent pure states based on a PLI rank-1 POVM. Finally, by properties of rank-1 POVMs and equioverlapping measurements, we give some relationships between weak values of an observable and its trace and expectations.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":"24 3","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2025-02-28","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/s11128-025-04685-x","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
In this article, we first obtain a characterization of relationships between pairwise linearly independent (PLI) rank-1 POVMs and Hamel bases for \({\mathbb {C}}^{d}\). By utilizing the obtained relationships, a necessary and sufficient condition is provided for the set of incoherent states based on PLI rank-1 POVM to be empty. Secondly, we deduce a detailed characterization of incoherent pure states based on a PLI rank-1 POVM. Finally, by properties of rank-1 POVMs and equioverlapping measurements, we give some relationships between weak values of an observable and its trace and expectations.
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.
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