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
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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。
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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.
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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.
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