# 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.