论文标题
表现出Kohen-Specker上下文的整数的最小环扩展
Minimal ring extensions of the integers exhibiting Kochen-Specker contextuality
论文作者
论文摘要
本文是对量子理论中情境性代数研究的贡献。作为Kochen和Specker的无隐性变量的代数类似物，我们调查了理性子环，其中$ d \ times d $ d $对称矩阵的部分环（$ d \ geq 3 $）不承认通勤环，我们认为这是“ Algebraic node sedind Stone”。对于$ d = 3 $，最小的戒指被证明为$ \ mathbb {z} [1/6] $，而对于$ d \ geq 6 $，最小subring为$ \ mathbb {z} $本身。这些证明依赖于没有高螺旋彩色的尺寸3和6中新的整数向量的构造。
This paper is a contribution to the algebraic study of contextuality in quantum theory. As an algebraic analogue of Kochen and Specker's no-hidden-variables result, we investigate rational subrings over which the partial ring of $d \times d$ symmetric matrices ($d \geq 3$) admits no morphism to a commutative ring, which we view as an "algebraic hidden state." For $d = 3$, the minimal such ring is shown to be $\mathbb{Z}[1/6]$, while for $d \geq 6$ the minimal subring is $\mathbb{Z}$ itself. The proofs rely on the construction of new sets of integer vectors in dimensions 3 and 6 that have no Kochen-Specker coloring.
