{"title":"Multipartite standard nonlocality sharing by m-sided independent sequential observers","authors":"Hao Sun, Fenzhuo Guo, Haifeng Dong, Fei Gao","doi":"10.1007/s11128-024-04460-4","DOIUrl":null,"url":null,"abstract":"<p>The sharing of quantum nonlocality has been the subject of much recent research for two-qubit and three-qubit entangled systems. In this paper, we discuss nonlocality sharing with unsharp measurement based on Mermin–Ardehali–Belinskii–Klyshko (MABK) inequality for the <i>N</i>-qubit generalized Greenberger–Horne–Zeilinger (GHZ) system. In the one-sided sequential measurements scenario, we determine a state range associated with <i>k</i> within which <span>\\( k+1 \\)</span> independent observers can share the standard <i>N</i>-partite nonlocality with the other <span>\\((N-1)\\)</span> sides, as well as a state range where arbitrarily many independent observers can do the same. Similarly, as to the <i>m</i>-sided sequential measurements scenario, we also identify a state range influenced by <i>k</i> within which <span>\\( k+1 \\)</span> independent observers in each of <i>m</i> sides can share the standard <i>N</i>-partite nonlocality with the other <span>\\((N-m)\\)</span> sides, and a state range where arbitrarily many independent observers can do so. Crucially, all of our nonlocality sharing findings result from a measurement strategy in which every sequential observer employs unequal sharpness measurements. As a special case, for the three-qubit maximally entangled GHZ state, we demonstrate that an unbounded number of observers can share the nonlocality in the one-sided sequential measurements scenario. This outcome further underscores the importance of unequal sharpness measurements in recycling qubits for generating quantum nonlocality.</p>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-06-24","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/s11128-024-04460-4","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
The sharing of quantum nonlocality has been the subject of much recent research for two-qubit and three-qubit entangled systems. In this paper, we discuss nonlocality sharing with unsharp measurement based on Mermin–Ardehali–Belinskii–Klyshko (MABK) inequality for the N-qubit generalized Greenberger–Horne–Zeilinger (GHZ) system. In the one-sided sequential measurements scenario, we determine a state range associated with k within which \( k+1 \) independent observers can share the standard N-partite nonlocality with the other \((N-1)\) sides, as well as a state range where arbitrarily many independent observers can do the same. Similarly, as to the m-sided sequential measurements scenario, we also identify a state range influenced by k within which \( k+1 \) independent observers in each of m sides can share the standard N-partite nonlocality with the other \((N-m)\) sides, and a state range where arbitrarily many independent observers can do so. Crucially, all of our nonlocality sharing findings result from a measurement strategy in which every sequential observer employs unequal sharpness measurements. As a special case, for the three-qubit maximally entangled GHZ state, we demonstrate that an unbounded number of observers can share the nonlocality in the one-sided sequential measurements scenario. This outcome further underscores the importance of unequal sharpness measurements in recycling qubits for generating quantum nonlocality.
量子非局域性的共享一直是近年来二量子比特和三量子比特纠缠系统研究的主题。本文基于 N 量子位广义格林伯格-霍恩-泽林格(GHZ)系统的 Mermin-Ardehali-Belinskii-Klyshko (MABK)不等式,讨论了非尖锐测量的非局域性共享。在单边顺序测量场景中,我们确定了一个与k相关的状态范围,在这个范围内,\( k+1 \)个独立观测者可以与其他\((N-1)\)边共享标准的N边非局域性,以及一个任意多个独立观测者都可以这样做的状态范围。同样,对于 m 边顺序测量的情况,我们也确定了一个受 k 影响的状态范围,在这个范围内,m 边中每边的\( k+1 \)个独立观察者可以与其他\((N-m)\)边共享标准的 N 边非位置性,还有一个任意多的独立观察者可以这样做的状态范围。最重要的是,我们所有的非局域性共享发现都来自于一种测量策略,在这种策略中,每个顺序观测者都采用了不相等的锐度测量。作为一个特例,对于三量子位最大纠缠 GHZ 状态,我们证明了在单边顺序测量的情况下,无限制数量的观察者可以共享非局域性。这一结果进一步强调了回收量子比特中不等锐度测量对产生量子非位置性的重要性。
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.