论文标题
量子映射和设计
Quantum mappings and designs
论文作者
论文摘要
为了使用量子设备进行计算，有必要了解理论描述的复杂性。为此，我们提供了几种可用于理解量子力学的新型结构，从映射和设计的角度来理解量子力学。在特定情况下，例如对于所有尺寸4的矩阵。此外，我们提供了一个明确的公式，用于在多部分情况下纠缠力量。最重要的是，该论文提出并详细说明了导致最近构建四个子系统六个级别的绝对最大纠缠状态的路径。最后，我们将基数研究作为量子拉丁正方形和量子sudoku（sudoq）的“量子性”的量度。最高基数的阵列产生了特殊特性的量子测量的家族。证明了Sudoq设计与互无偏基的联系。
In order to use quantum devices for computations, it is necessary to understand the intricacies of the theoretical description. To this end, we provide several novel constructions useful for the comprehension of quantum mechanics from the perspective of mappings and designs. The unistochasticity problem, which relates the classical and the quantum domain, is solved in specific cases, e.g. for all matrices of dimension 4. Furthermore, we provide an explicit formula for entangling power in the multipartite case. Most importantly, the thesis presents and elaborates on the path that lead to the recent construction of absolutely maximally entangled state of four subsystems six levels each. Finally, we study cardinality as a measure of "quantumness" of quantum Latin squares and quantum Sudoku (SudoQ). Arrays of the highest cardinality yield families of quantum measurements of special properties. A connection between SudoQ designs and mutually unbiased bases is demonstrated.
