Pavičić Mladen
Center of Excellence for Advanced Materials and Sensors, Research Unit Photonics and Quantum Optics, Institute Ruđer Bošković, 10000 Zagreb, Croatia.
Institute of Physics, 10000 Zagreb, Croatia.
Entropy (Basel). 2023 Jul 26;25(8):1117. doi: 10.3390/e25081117.
Quantum contextuality supports quantum computation and communication. One of its main vehicles is hypergraphs. The most elaborated are the Kochen-Specker ones, but there is also another class of contextual sets that are not of this kind. Their representation has been mostly operator-based and limited to special constructs in three- to six-dim spaces, a notable example of which is the Yu-Oh set. Previously, we showed that hypergraphs underlie all of them, and in this paper, we give general methods-whose complexity does not scale up with the dimension-for generating such non-Kochen-Specker hypergraphs in any dimension and give examples in up to 16-dim spaces. Our automated generation is probabilistic and random, but the statistics of accumulated data enable one to filter out sets with the required size and structure.
量子语境性支持量子计算与通信。其主要载体之一是超图。最详尽的是科亨 - 斯佩克超图，但也存在另一类并非此类的语境集。它们的表示大多基于算子，且局限于三维至六维空间中的特殊结构，其中一个显著例子是柳 - 吴集。此前，我们表明超图是所有这些的基础，在本文中，我们给出了通用方法——其复杂度不随维度增加——用于在任意维度生成此类非科亨 - 斯佩克超图，并给出了高达16维空间的示例。我们的自动生成是概率性且随机的，但累积数据的统计信息使人们能够筛选出具有所需大小和结构的集合。
