Generalized Matrix Functions and Geometric Measure of Entanglement

Given a complex n × n matrix A and an irreducible character χ of permutation group on n letters, generalized matrix function d _χ (A) of A can be thought as combinatorial generalization of matrix permanent and determinant. Due to its combinatorial nature, it is usually a demanding task to assign the construction some geometrical meaning. In this presentation, we discuss how generalized matrix functions serve as essential tools in determining geometric measure of entanglement of certain quantum states. Along the way, we obtain some unexpected geometric interpretations and investigate some examples.