# Codes and Expansions (CodEx) Seminar

## Shujie Kang (University of Texas at Arlington)Non-informationally complete Gabor POVMs

A POVM (positive operator valued measure) is informationally complete if the $d^2$ corresponding rank 1 matrices form a basis for the space of $d\times d$ matrices. Generically Gabor POVMs are informationally complete. We classify non-informationally complete Gabor POVMs and describe some properties of them. We also use the result to construct sets of $d^2$ unit vectors in $\mathbb{C}^d$ with a relatively smaller number of distinct inner products.