论文标题
魔法正方形：拉丁语，半经典和量子
Magic squares: Latin, Semiclassical and Quantum
论文作者
论文摘要
量子魔法正方形最近被引入量子测量的“神奇”组合。与量子测量值相反，它们不能纯化（即扩张至量子置换矩阵） - 只有所谓的半经典词可以。纯化建立了与理想理论和实际重要性的理想世界的关系；纯化的相反由矩阵凸壳描述。在这项工作中，我们证明了半经典的魔法正方形可以纯化为量子拉丁正方形，这是正交碱基的“魔术”组合。相反，我们证明量子拉丁正方形的矩阵凸壳比半经典的壳体大。我们的第三个结果解决了这种张力：我们证明了半经典的量子拉丁正方形恰好是由经典拉丁方形构建的量子。我们的作品阐明了量子魔法正方形的内部结构，这是如何受到矩阵凸壳的影响的，以及在半经典和量子水平上的“魔法”组成规则的性质。
Quantum magic squares were recently introduced as a 'magical' combination of quantum measurements. In contrast to quantum measurements, they cannot be purified (i.e. dilated to a quantum permutation matrix) -- only the so-called semiclassical ones can. Purifying establishes a relation to an ideal world of fundamental theoretical and practical importance; the opposite of purifying is described by the matrix convex hull. In this work, we prove that semiclassical magic squares can be purified to quantum Latin squares, which are 'magical' combinations of orthonormal bases. Conversely, we prove that the matrix convex hull of quantum Latin squares is larger than the semiclassical ones. This tension is resolved by our third result: We prove that the quantum Latin squares that are semiclassical are precisely those constructed from a classical Latin square. Our work sheds light on the internal structure of quantum magic squares, on how this is affected by the matrix convex hull, and, more generally, on the nature of the 'magical' composition rule, both at the semiclassical and quantum level.
