最小场景中的量子关联

最小场景中的量子关联

时间戳记：16年2023月9日上午18:XNUMX
源节点： 2527781

盛普·勒1, 基娅拉梅罗尼2, 伯恩德·斯特姆费尔斯3,4, 莱因哈德 F.维尔纳5, 和蒂莫·齐格勒5

1维也纳量子光学和量子信息研究所，Boltzmanngasse 3 1090 Vienna, Austria
2数学计算与实验研究所，121 South Main Street Providence RI 02903，美国
3马克斯·普朗克莱比锡科学数学研究所，Inselstrasse 22 04103 Leipzig, Germany
4加州大学伯克利分校数学系，970 Evans Hall #3840 Berkeley CA 94720-3840，美国
5Insitute für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2 30167 Hannover, 德国

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抽象

在量子相关的最小场景中，双方可以从两个可观察到的结果中进行选择，每个可观察到的结果有两个。 概率由四个边缘和四个相关性指定。 由此产生的四维凸相关体，表示为 $mathcal{Q}$，是量子信息论的基础。 我们回顾并系统化了有关 $mathcal{Q}$ 的知识，并添加了许多细节、可视化和完整的证明。 特别是，我们提供了边界的详细描述，边界由与椭圆同构的三维面和暴露的极值点的六次代数流形组成。 这些补丁由未暴露的极值点的立方体表面分开。 我们提供所有极值点的三角参数化，以及它们暴露的 Tsirelson 不等式和量子模型。 所有非经典极值点（暴露与否）都是自测的，即由本质上独特的量子模型实现。
Two principles, which are specific to the minimal scenario, allow a quick and complete overview: The first is the pushout transformation, i.e., the application of the sine function to each coordinate. This transforms the classical correlation polytope exactly into the correlation body $mathcal{Q}$, also identifying the boundary structures. The second principle, self-duality, is an isomorphism between $mathcal{Q}$ and its polar dual, i.e., the set of affine inequalities satisfied by all quantum correlations (“Tsirelson inequalities''). The same isomorphism links the polytope of classical correlations contained in $mathcal{Q}$ to the polytope of no-signalling correlations, which contains $mathcal{Q}$.
我们还讨论了通过固定希尔伯特空间维度、固定状态或固定可观察量实现的相关集，并为涉及相关矩阵行列式的 $mathcal{Q}$ 建立了一个新的非线性不等式。

特色图片：三个相关集的关系：经典和无信号多胞体（左）和量子集（右，橙色）。

热门摘要

自量子理论诞生以来，表征和理解一组允许的量子相关性一直是一个重要目标。 在这项工作中，我们从几何和应用等几个角度对最小的非平凡场景中的量子关联集提供了最全面的理解。 我们用大量的三个维度的精确可视化来补充我们的理论理解。

►BibTeX数据

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被引用

[1] Antoni Mikos-Nuszkiewicz 和 Jędrzej Kaniewski，“CHSH 场景中量子集的极值点：猜想的解析解”， 的arXiv：2302.10658, (2023).

[2] José Jesus and Emmanuel Zambrini Cruzeiro, "Tight Bell inequalities from polytope slices", 的arXiv：2212.03212, (2022).

[3] Rafael Wagner, Rui Soares Barbosa, and Ernesto F. Galvão, "Inequalities witnessing coherence, nonlocality, and contextuality", 的arXiv：2209.02670, (2022).

[4] Lina Vandré and Marcelo Terra Cunha, "Quantum sets of the multicolored-graph approach to contextuality", 物理评论A 106 6，062210（2022）.

以上引用来自 SAO / NASA广告 （最近成功更新为2023-03-22 14:01:01）。 该列表可能不完整，因为并非所有发布者都提供合适且完整的引用数据。

On Crossref 的引用服务 找不到有关引用作品的数据（上一次尝试2023-03-22 14:00:59）。

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