Meng-Ya Dong, Su-Juan Zhang, Chen-Ming Bai, Lu Liu
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Subsequently, based on the partitioning mode, nonlocal orthogonal product states in <inline-formula>\n<tex-math><?CDATA $ (\\mathbb{C}^{3})^{\\otimes 6 }$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mo>⊗</mml:mo><mml:mn>6</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"lplad3817ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> and <inline-formula>\n<tex-math><?CDATA $(\\mathbb{C}^{4})^{\\otimes 6 }$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">C</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mo>⊗</mml:mo><mml:mn>6</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"lplad3817ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> are given. Finally, we construct nonlocal orthogonal product states in <inline-formula>\n<tex-math><?CDATA $(\\mathbb{C}^{d})^{\\otimes 2n}$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">C</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup><mml:msup><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mo>⊗</mml:mo><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"lplad3817ieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> and discuss the cases where <italic toggle=\"yes\">d</italic> is odd and even. Our results demonstrate the phenomenon of nonlocality without entanglement in a 2<italic toggle=\"yes\">n</italic>-partite system.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantum nonlocality without entanglement in a 2n-partite system\",\"authors\":\"Meng-Ya Dong, Su-Juan Zhang, Chen-Ming Bai, Lu Liu\",\"doi\":\"10.1088/1612-202x/ad3817\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In recent years, researchers focused their attention on the construction of nonlocal product states in multipartite quantum systems. This paper proposes a novel partitioning method for multipartite quantum systems, aiming to improve the operation efficiency. Firstly, we divide 2<italic toggle=\\\"yes\\\">n</italic> subsystems into <italic toggle=\\\"yes\\\">n</italic> parts two by two and implement orthogonality-preserving local measurement on the partitioned composite systems. Subsequently, based on the partitioning mode, nonlocal orthogonal product states in <inline-formula>\\n<tex-math><?CDATA $ (\\\\mathbb{C}^{3})^{\\\\otimes 6 }$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\\\"double-struck\\\">C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mo stretchy=\\\"false\\\">)</mml:mo><mml:mrow><mml:mo>⊗</mml:mo><mml:mn>6</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"lplad3817ieqn1.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> and <inline-formula>\\n<tex-math><?CDATA $(\\\\mathbb{C}^{4})^{\\\\otimes 6 }$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\\\"double-struck\\\">C</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mo stretchy=\\\"false\\\">)</mml:mo><mml:mrow><mml:mo>⊗</mml:mo><mml:mn>6</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"lplad3817ieqn2.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> are given. Finally, we construct nonlocal orthogonal product states in <inline-formula>\\n<tex-math><?CDATA $(\\\\mathbb{C}^{d})^{\\\\otimes 2n}$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\\\"double-struck\\\">C</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup><mml:msup><mml:mo stretchy=\\\"false\\\">)</mml:mo><mml:mrow><mml:mo>⊗</mml:mo><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"lplad3817ieqn3.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> and discuss the cases where <italic toggle=\\\"yes\\\">d</italic> is odd and even. Our results demonstrate the phenomenon of nonlocality without entanglement in a 2<italic toggle=\\\"yes\\\">n</italic>-partite system.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-04-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1612-202x/ad3817\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1612-202x/ad3817","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
近年来，研究人员将注意力集中在多方量子系统中非局域积态的构建上。本文提出了一种新颖的多方量子系统划分方法，旨在提高运行效率。首先，我们将 2n 个子系统两两分割成 n 个部分，并在分割后的复合系统上实现正交保全局部测量。然后，根据分割模式，给出 (C3)⊗6 和 (C4)⊗6 中的非局部正交积状态。最后，我们构建了 (Cd)⊗2n 中的非局部正交积状态，并讨论了 d 为奇数和偶数的情况。我们的结果证明了在 2n 对偶系统中没有纠缠的非局域现象。
Quantum nonlocality without entanglement in a 2n-partite system
In recent years, researchers focused their attention on the construction of nonlocal product states in multipartite quantum systems. This paper proposes a novel partitioning method for multipartite quantum systems, aiming to improve the operation efficiency. Firstly, we divide 2n subsystems into n parts two by two and implement orthogonality-preserving local measurement on the partitioned composite systems. Subsequently, based on the partitioning mode, nonlocal orthogonal product states in (C3)⊗6 and (C4)⊗6 are given. Finally, we construct nonlocal orthogonal product states in (Cd)⊗2n and discuss the cases where d is odd and even. Our results demonstrate the phenomenon of nonlocality without entanglement in a 2n-partite system.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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