论文标题
9 $ \ times $ 4 = 6 $ \ times $ 6：了解36名军官的欧拉问题的量子解决方案
9 $\times$ 4 = 6 $\times$ 6: Understanding the quantum solution to the Euler's problem of 36 officers
论文作者
论文摘要
欧拉（Euler）的著名组合问题涉及从$ 6 \ tims 6 $ square Array的六个不同团中的$ 36 $官员的安排。每个团由六个属于六个等级之一的军官组成。起源于圣彼得堡的问题要求每行和阵列的每一列仅包含一个给定等级的一名官员和给定的团。 Euler观察到这种配置不存在。在最近的工作中，我们为该问题的量子版本构建了一个解决方案，假设官员对应于量子状态，并且可以纠缠。在本文中，我们解释了基于36名官员分为9个组的解决方案，每个官员都有四个要素。相应的量子状态在当地等同于最大纠结的两分Quibit状态，因此每个官员在他的35美元同事中最多都纠缠在一起。整个量子组合设计涉及$ 9 $铃铛基础的九个补充$ 4 $维度子空间。
The famous combinatorial problem of Euler concerns an arrangement of $36$ officers from six different regiments in a $6 \times 6$ square array. Each regiment consists of six officers each belonging to one of six ranks. The problem, originating from Saint Petersburg, requires that each row and each column of the array contains only one officer of a given rank and given regiment. Euler observed that such a configuration does not exist. In recent work, we constructed a solution to a quantum version of this problem assuming that the officers correspond to quantum states and can be entangled. In this paper, we explain the solution which is based on a partition of 36 officers into nine groups, each with four elements. The corresponding quantum states are locally equivalent to maximally entangled two-qubit states, hence each officer is entangled with at most three out of his $35$ colleagues. The entire quantum combinatorial design involves $9$ Bell bases in nine complementary $4$-dimensional subspaces.
