ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

In minisymposium: Linear Algebra and Quantum Computation

Tue 16:30–17:00, Auditorium Jean Monnet
Generalized matrix functions and geometric measure of entanglement.
Vehbi Paksoy (Nova Southeastern University)
Joint work with Fuzhen Zhang, Haixia Chang

Given a complex $n\times n$ matrix $A$ and an irreducible character $\chi$ of permutation group on $n$ letters, generalized matrix function $d_{\chi}(A)$ 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.