人鱼多面体量子计算与基础

IF 0.7 4区 物理与天体物理 Q3 COMPUTER SCIENCE, THEORY & METHODS Quantum Information & Computation Pub Date : 2023-07-01 DOI:10.26421/qic23.9-10-2
Cihan Okay, Ho Yiu Chung, Selman Ipek
{"title":"人鱼多面体量子计算与基础","authors":"Cihan Okay, Ho Yiu Chung, Selman Ipek","doi":"10.26421/qic23.9-10-2","DOIUrl":null,"url":null,"abstract":"Mermin square scenario provides a simple proof for state-independent contextuality. In this paper, we study polytopes $\\MP_\\beta$ obtained from the Mermin scenario, parametrized by a function $\\beta$ on the set of contexts. Up to combinatorial isomorphism, there are two types of polytopes $\\MP_0$ and $\\MP_1$ depending on the parity of $\\beta$. Our main result is the classification of the vertices of these two polytopes. In addition, we describe the graph associated with the polytopes. All the vertices of $\\MP_0$ turn out to be deterministic. This result provides a new topological proof of a celebrated result of Fine characterizing noncontextual distributions on the CHSH scenario. $\\MP_1$ can be seen as a nonlocal toy version of $\\Lambda$-polytopes, a class of polytopes introduced for the simulation of universal quantum computation. In the $2$-qubit case, we provide a decomposition of the $\\Lambda$-polytope using $\\MP_1$, whose vertices are classified, and the nonsignaling polytope of the $(2,3,2)$ Bell scenario, whose vertices are well-known.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"31 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mermin polytopes quantum computation and foundations\",\"authors\":\"Cihan Okay, Ho Yiu Chung, Selman Ipek\",\"doi\":\"10.26421/qic23.9-10-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Mermin square scenario provides a simple proof for state-independent contextuality. In this paper, we study polytopes $\\\\MP_\\\\beta$ obtained from the Mermin scenario, parametrized by a function $\\\\beta$ on the set of contexts. Up to combinatorial isomorphism, there are two types of polytopes $\\\\MP_0$ and $\\\\MP_1$ depending on the parity of $\\\\beta$. Our main result is the classification of the vertices of these two polytopes. In addition, we describe the graph associated with the polytopes. All the vertices of $\\\\MP_0$ turn out to be deterministic. This result provides a new topological proof of a celebrated result of Fine characterizing noncontextual distributions on the CHSH scenario. $\\\\MP_1$ can be seen as a nonlocal toy version of $\\\\Lambda$-polytopes, a class of polytopes introduced for the simulation of universal quantum computation. In the $2$-qubit case, we provide a decomposition of the $\\\\Lambda$-polytope using $\\\\MP_1$, whose vertices are classified, and the nonsignaling polytope of the $(2,3,2)$ Bell scenario, whose vertices are well-known.\",\"PeriodicalId\":54524,\"journal\":{\"name\":\"Quantum Information & Computation\",\"volume\":\"31 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Information & Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26421/qic23.9-10-2\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information & Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26421/qic23.9-10-2","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0

摘要

人鱼广场场景为独立于状态的上下文性提供了一个简单的证明。在本文中,我们研究了从Mermin场景中得到的多面体$\MP_\beta$,在上下文集合上用一个函数$\beta$参数化。直到组合同构为止,根据$\beta$的宇称,有两种类型的多面体$\MP_0$和$\MP_1$。我们的主要结果是这两个多面体的顶点的分类。此外,我们还描述了与多面体相关的图。$\MP_0$的所有顶点都是确定性的。这个结果为Fine在CHSH场景中描述非上下文分布的著名结果提供了一个新的拓扑证明。$\MP_1$可以看作是$\Lambda$ -多面体的非局部玩具版本,这是一类为模拟通用量子计算而引入的多面体。在$2$ -qubit情况下,我们使用$\MP_1$(其顶点是分类的)和$(2,3,2)$ Bell场景的非信号多角体(其顶点是众所周知的)对$\Lambda$ -多角体进行分解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Mermin polytopes quantum computation and foundations
Mermin square scenario provides a simple proof for state-independent contextuality. In this paper, we study polytopes $\MP_\beta$ obtained from the Mermin scenario, parametrized by a function $\beta$ on the set of contexts. Up to combinatorial isomorphism, there are two types of polytopes $\MP_0$ and $\MP_1$ depending on the parity of $\beta$. Our main result is the classification of the vertices of these two polytopes. In addition, we describe the graph associated with the polytopes. All the vertices of $\MP_0$ turn out to be deterministic. This result provides a new topological proof of a celebrated result of Fine characterizing noncontextual distributions on the CHSH scenario. $\MP_1$ can be seen as a nonlocal toy version of $\Lambda$-polytopes, a class of polytopes introduced for the simulation of universal quantum computation. In the $2$-qubit case, we provide a decomposition of the $\Lambda$-polytope using $\MP_1$, whose vertices are classified, and the nonsignaling polytope of the $(2,3,2)$ Bell scenario, whose vertices are well-known.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Quantum Information & Computation
Quantum Information & Computation 物理-计算机:理论方法
CiteScore
1.70
自引率
0.00%
发文量
42
审稿时长
3.3 months
期刊介绍: Quantum Information & Computation provides a forum for distribution of information in all areas of quantum information processing. Original articles, survey articles, reviews, tutorials, perspectives, and correspondences are all welcome. Computer science, physics and mathematics are covered. Both theory and experiments are included. Illustrative subjects include quantum algorithms, quantum information theory, quantum complexity theory, quantum cryptology, quantum communication and measurements, proposals and experiments on the implementation of quantum computation, communications, and entanglement in all areas of science including ion traps, cavity QED, photons, nuclear magnetic resonance, and solid-state proposals.
期刊最新文献
Closed-form analytic expressions for shadow estimation with brickwork circuits Dynamics of one two-level-atom interacting with a multiple cavity modes Fast naviation with icosahedral golden gates Many-body quantum state control in the presence of environmental noise A simpler security proof for 6-state quantum key distribution
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1