Zero entries in multipartite product unitary matrices

Characterizing the zero entries in multipartite unitary matrices plays an important role in evaluating the usefulness of such matrices in quantum information. We investigate the zero entries in unitary and product unitary matrices. On one hand, we study the quantity properties of the zero entries in the multiqubit and bipartite product unitary matrices, respectively. We also investigate the ratio of the number of elements in the set made up of the numbers of zero entries in product unitary matrices to the number of all cases of such entries. On the other hand, we focus on the distribution of zero entries in unitary and product unitary matrices. Our results help identify whether a matrix containing at least one zero entry is a unitary matrix.