论文标题
自动生成任意许多Kochen-Specker和其他上下文集中的奇数希尔伯特空间
Automated Generation of Arbitrarily Many Kochen-Specker and Other Contextual Sets in Odd Dimensional Hilbert Spaces
论文作者
论文摘要
量子计算和通信的开发，最近证明是由情境性支持的，可以说是要求上下文集的必要供应。虽然在什至维度空间中实现了这一点，但在奇数空间中，到目前为止，仅找到了十几个临界Kochen-Specker（KS）集。在本文中，我们提供了三种方法，用于在任何维度上任意生成许多上下文的KS和NON-KS集，以实现未来的应用和实施，我们采用它们来获取数百万的KS和其他上下文集中在维度3、5、7和9中，以前只有少数集合已经找到了一些集合。同样，到目前为止，尚无针对原始Kochen-Specker集的明确向量，而我们现在从24个向量组件中生成它们。
Development of quantum computation and communication, recently shown to be supported by contextuality, arguably asks for a requisite supply of contextual sets. While that has been achieved in even dimensional spaces, in odd dimensional spaces only a dozen contextual critical Kochen-Specker (KS) sets have been found so far. In this paper we give three methods for automated generation of arbitrarily many contextual KS and non-KS sets in any dimension for possible future application and implementation and we employ them to obtain millions of KS and other contextual sets in dimensions 3, 5, 7, and 9 where previously only a handful of sets have been found. Also, no explicit vectors for the original Kochen-Specker set were known so far, while we now generate them from 24 vector components.
