Algebraic Graph Theory Seminar - Chris Godsil

Title: Quantum Latin Squares and Magic Unitaries

Abstract:

A quantum Latin square is an n x n array of vectors such that vectors in any row or any column form an orthonormal basis for Cⁿ. A magic unitary matrix is an n x n array of projections such that each row and column sums to I. (Such matrices are necessarily unitary, as we will see, and can be constructed from quantum Latin squares.) I will discuss constructions of these matrices and some of their applications, including a connection to quantum automorphisms of graphs.