A mathematical result suggested by Euler in the 18th century and first proved in the 19th century says that there is no pair of orthogonal Latin squares of order 6. Another 100 years later, mathematicians and physicists studying quantum entanglement suggested a quantum variant of the problem: Here, a pair of orthogonal quantum Latin squares corresponds to a particular unitary operator acting on a tensor product of finite vector spaces. Surprisingly, it was proved very recently that there exist quantum orthogonal Latin squares of order 6. Besides this being a nice puzzle, there are many applications of quantum orthogonal Latin squares in the theory of entanglement and to design quantum error correcting codes for quantum computation. The goal of the project is to understand these fascinating results and to learn about their connections to other parts of quantum information science.
Prerequisite knowledge: