{"title":"Local discrimination of lattice states via adjacent matrix","authors":"Ying-Hui Yang, Qi-Yue Zhao, Pei-Ying Chen, Shi-Jiao Geng, Jiang-Tao Yuan","doi":"10.1007/s11128-024-04436-4","DOIUrl":null,"url":null,"abstract":"<p>We investigate the distinguishability of lattice states by local operations and classical communication (LOCC) in <span>\\({\\mathbb {C}}^{p^{r}}\\otimes {\\mathbb {C}}^{p^{r}}\\)</span>, where <i>p</i> is a prime. Firstly, for all the lattice matrices, we present that there are <span>\\(\\prod _{a=1}^{r}(p^{a}+1)\\)</span> number of distinct maximal commuting sets. Secondly, we give a criterion to determine the local discrimination of lattice states via adjacent matrix. The previous results (Phys Rev A 92:042320, 2015; Phys Scr 98:115102, 2023) can be covered by our result. Finally, we give a sufficient condition for LOCC indistinguishability of <span>\\(p^{r}\\)</span> lattice states.\n</p>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information Processing","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s11128-024-04436-4","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
We investigate the distinguishability of lattice states by local operations and classical communication (LOCC) in \({\mathbb {C}}^{p^{r}}\otimes {\mathbb {C}}^{p^{r}}\), where p is a prime. Firstly, for all the lattice matrices, we present that there are \(\prod _{a=1}^{r}(p^{a}+1)\) number of distinct maximal commuting sets. Secondly, we give a criterion to determine the local discrimination of lattice states via adjacent matrix. The previous results (Phys Rev A 92:042320, 2015; Phys Scr 98:115102, 2023) can be covered by our result. Finally, we give a sufficient condition for LOCC indistinguishability of \(p^{r}\) lattice states.
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.