Ling-Hui Zhu, Zhen Zhu, Guo-Lin Lv, Chong-Qiang Ye, Xiao-Yu Chen
{"title":"Dicke-W 和 Greenberger-Horne-Zeilinger 混合态纠缠的鲁棒性。","authors":"Ling-Hui Zhu, Zhen Zhu, Guo-Lin Lv, Chong-Qiang Ye, Xiao-Yu Chen","doi":"10.3390/e26090804","DOIUrl":null,"url":null,"abstract":"<p><p>Quantum entanglement is a fundamental characteristic of quantum mechanics, and understanding the robustness of entanglement across different mixed states is crucial for comprehending the entanglement properties of general quantum states. In this paper, the robustness of entanglement of Dicke-W and Greenberger-Horne-Zeilinger (GHZ) mixed states under different mixing ratios is calculated using the entanglement witness method. The robustnesses of entanglement of Dicke-W and GHZ mixed states are different when the probability ratio of Dicke to W is greater than 32 and less than 32. For the probability of Dicke and W states greater than or equal to 32, we study the robustness of entanglement of Dicke and GHZ mixed states and analyze and calculate their upper and lower bounds. For the probability of Dicke and W states less than 32, we take the equal probability ratio of Dicke and W states as an example and calculate and analyze the upper and lower bounds of their robustness of entanglement in detail.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"26 9","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11431323/pdf/","citationCount":"0","resultStr":"{\"title\":\"Robustness of Entanglement for Dicke-W and Greenberger-Horne-Zeilinger Mixed States.\",\"authors\":\"Ling-Hui Zhu, Zhen Zhu, Guo-Lin Lv, Chong-Qiang Ye, Xiao-Yu Chen\",\"doi\":\"10.3390/e26090804\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Quantum entanglement is a fundamental characteristic of quantum mechanics, and understanding the robustness of entanglement across different mixed states is crucial for comprehending the entanglement properties of general quantum states. In this paper, the robustness of entanglement of Dicke-W and Greenberger-Horne-Zeilinger (GHZ) mixed states under different mixing ratios is calculated using the entanglement witness method. The robustnesses of entanglement of Dicke-W and GHZ mixed states are different when the probability ratio of Dicke to W is greater than 32 and less than 32. For the probability of Dicke and W states greater than or equal to 32, we study the robustness of entanglement of Dicke and GHZ mixed states and analyze and calculate their upper and lower bounds. For the probability of Dicke and W states less than 32, we take the equal probability ratio of Dicke and W states as an example and calculate and analyze the upper and lower bounds of their robustness of entanglement in detail.</p>\",\"PeriodicalId\":11694,\"journal\":{\"name\":\"Entropy\",\"volume\":\"26 9\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-09-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11431323/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Entropy\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.3390/e26090804\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Entropy","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.3390/e26090804","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
量子纠缠是量子力学的一个基本特征,了解不同混合态下纠缠的鲁棒性对于理解一般量子态的纠缠特性至关重要。本文利用纠缠见证法计算了 Dicke-W 和 Greenberger-Horne-Zeilinger (GHZ) 混合态在不同混合比下的纠缠鲁棒性。当 Dicke 与 W 的概率比大于 32 和小于 32 时,Dicke-W 和 GHZ 混合态的纠缠鲁棒性是不同的。当 Dicke 和 W 状态的概率大于或等于 32 时,我们研究了 Dicke 和 GHZ 混合状态纠缠的鲁棒性,并分析计算了它们的上下限。对于小于 32 的 Dicke 和 W 状态的概率,我们以 Dicke 和 W 状态的等概率比为例,详细地计算和分析了它们的纠缠鲁棒性的上界和下界。
Robustness of Entanglement for Dicke-W and Greenberger-Horne-Zeilinger Mixed States.
Quantum entanglement is a fundamental characteristic of quantum mechanics, and understanding the robustness of entanglement across different mixed states is crucial for comprehending the entanglement properties of general quantum states. In this paper, the robustness of entanglement of Dicke-W and Greenberger-Horne-Zeilinger (GHZ) mixed states under different mixing ratios is calculated using the entanglement witness method. The robustnesses of entanglement of Dicke-W and GHZ mixed states are different when the probability ratio of Dicke to W is greater than 32 and less than 32. For the probability of Dicke and W states greater than or equal to 32, we study the robustness of entanglement of Dicke and GHZ mixed states and analyze and calculate their upper and lower bounds. For the probability of Dicke and W states less than 32, we take the equal probability ratio of Dicke and W states as an example and calculate and analyze the upper and lower bounds of their robustness of entanglement in detail.
期刊介绍:
Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.