论文标题
Euler问题的量子版本：几何视角
Quantum version of the Euler's problem: a geometric perspective
论文作者
论文摘要
$ 36 $官员的经典组合问题没有解决方案，因为没有第六订单的graeco-latin正方形。如果一个人在量子设置中工作并允许经典对象的叠加并接收纠缠状态，情况就会发生变化。我们从几何学角度分析了最近发现的Euler问题量子版本的解决方案。回忆起嵌入在较大空间中的不可移位的歧管的概念。该属性意味着这种歧管的任何两个副本，例如球体上的两个大圆圈，都相交。存在六个尺寸的量子graeco -latin平方，相当于具有D = 6级的四个子系统的最大纠缠状态，这意味着三个副本u（36）/u（36）/u（36）/u（36）/u（36）/u（1）的最大纠缠状态的$ 36 \ times 36 \ times 36 $ system empeds $ 36 $ systec $ {36.366同时在某个时刻。
The classical combinatorial problem of $36$ officers has no solution, as there are no Graeco-Latin squares of order six. The situation changes if one works in a quantum setup and allows for superpositions of classical objects and admits entangled states. We analyze the recently found solution to the quantum version of the Euler's problem from a geometric point of view. The notion of a non-displaceable manifold embedded in a larger space is recalled. This property implies that any two copies of such a manifold, like two great circles on a sphere, do intersect. Existence of a quantum Graeco-Latin square of size six, equivalent to a maximally entangled state of four subsystems with d=6 levels each, implies that three copies of the manifold U(36)/U(1) of maximally entangled states of the $36\times 36$ system, embedded in the complex projective space ${C}P^{36\times 36 -1}$, do intersect simultaneously at a certain point.
