{"title":"Gisin优雅贝尔不等式最大量子违反的紧上界及其在随机性证明中的应用","authors":"Dan-Dan Hu, Meng-Yan Li, Fen-Zhuo Guo, Yu-Kun Wang, Hai-Feng Dong, Fei Gao","doi":"10.1140/epjqt/s40507-025-00325-6","DOIUrl":null,"url":null,"abstract":"<div><p>The violation of a Bell inequality implies the existence of nonlocality, making device-independent randomness certification possible. This paper derives a tight upper bound for the maximal quantum violation of Gisin’s elegant Bell inequality (EBI) for arbitrary two-qubit states, along with the constraints required to achieve this bound. This method provides the necessary and sufficient conditions for violating the EBI for several quantum states, including pure two-qubit states and the Werner states. The lower bound of certifiable global randomness is analyzed based on the tight upper bound of the EBI for pure two-qubit states, with a comparison to the Clauser-Horne-Shimony-Holt (CHSH) inequality. The relationship between the noise level and the lower bound of certifiable global randomness with respect to the Werner states is also explored, and the comparisons with both the CHSH inequality and the chained inequality are given. The results indicate that when the state approaches a maximally entangled state within specific quantified ranges, the EBI demonstrates advantages over both the CHSH inequality and the chained inequality, providing theoretical guidance for experimental device-independent quantum random number generation.</p></div>","PeriodicalId":547,"journal":{"name":"EPJ Quantum Technology","volume":"12 1","pages":""},"PeriodicalIF":5.8000,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://epjquantumtechnology.springeropen.com/counter/pdf/10.1140/epjqt/s40507-025-00325-6","citationCount":"0","resultStr":"{\"title\":\"Tight upper bound of the maximal quantum violation of Gisin’s elegant Bell inequality and its application in randomness certification\",\"authors\":\"Dan-Dan Hu, Meng-Yan Li, Fen-Zhuo Guo, Yu-Kun Wang, Hai-Feng Dong, Fei Gao\",\"doi\":\"10.1140/epjqt/s40507-025-00325-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The violation of a Bell inequality implies the existence of nonlocality, making device-independent randomness certification possible. This paper derives a tight upper bound for the maximal quantum violation of Gisin’s elegant Bell inequality (EBI) for arbitrary two-qubit states, along with the constraints required to achieve this bound. This method provides the necessary and sufficient conditions for violating the EBI for several quantum states, including pure two-qubit states and the Werner states. The lower bound of certifiable global randomness is analyzed based on the tight upper bound of the EBI for pure two-qubit states, with a comparison to the Clauser-Horne-Shimony-Holt (CHSH) inequality. The relationship between the noise level and the lower bound of certifiable global randomness with respect to the Werner states is also explored, and the comparisons with both the CHSH inequality and the chained inequality are given. The results indicate that when the state approaches a maximally entangled state within specific quantified ranges, the EBI demonstrates advantages over both the CHSH inequality and the chained inequality, providing theoretical guidance for experimental device-independent quantum random number generation.</p></div>\",\"PeriodicalId\":547,\"journal\":{\"name\":\"EPJ Quantum Technology\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":5.8000,\"publicationDate\":\"2025-02-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://epjquantumtechnology.springeropen.com/counter/pdf/10.1140/epjqt/s40507-025-00325-6\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"EPJ Quantum Technology\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1140/epjqt/s40507-025-00325-6\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"OPTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPJ Quantum Technology","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1140/epjqt/s40507-025-00325-6","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPTICS","Score":null,"Total":0}
Tight upper bound of the maximal quantum violation of Gisin’s elegant Bell inequality and its application in randomness certification
The violation of a Bell inequality implies the existence of nonlocality, making device-independent randomness certification possible. This paper derives a tight upper bound for the maximal quantum violation of Gisin’s elegant Bell inequality (EBI) for arbitrary two-qubit states, along with the constraints required to achieve this bound. This method provides the necessary and sufficient conditions for violating the EBI for several quantum states, including pure two-qubit states and the Werner states. The lower bound of certifiable global randomness is analyzed based on the tight upper bound of the EBI for pure two-qubit states, with a comparison to the Clauser-Horne-Shimony-Holt (CHSH) inequality. The relationship between the noise level and the lower bound of certifiable global randomness with respect to the Werner states is also explored, and the comparisons with both the CHSH inequality and the chained inequality are given. The results indicate that when the state approaches a maximally entangled state within specific quantified ranges, the EBI demonstrates advantages over both the CHSH inequality and the chained inequality, providing theoretical guidance for experimental device-independent quantum random number generation.
期刊介绍:
Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics.
EPJ Quantum Technology covers theoretical and experimental advances in subjects including but not limited to the following:
Quantum measurement, metrology and lithography
Quantum complex systems, networks and cellular automata
Quantum electromechanical systems
Quantum optomechanical systems
Quantum machines, engineering and nanorobotics
Quantum control theory
Quantum information, communication and computation
Quantum thermodynamics
Quantum metamaterials
The effect of Casimir forces on micro- and nano-electromechanical systems
Quantum biology
Quantum sensing
Hybrid quantum systems
Quantum simulations.