Separability Properties for a Class of Block Matrices

Abstract

It is shown that, for the block matrices belonging to $M(nd,\mathbb{C})$ with commuting and normal block entries of dimension $d$, the separability of such a block matrices is equivalent to its semi-positive definity. The separability decomposition of lenght equal to the dimension of the block matrix (which is smaller then Carathéodory theorem implies) is given. The separability decomposition depends only on eigenvalues of block entries in the first part and on eigenvectors of the block entries in the second part of the tensor product. It is shown that semi-positive definity of considered block matrices is equivalent to semi-positive definity $d$ smaller matrices of dimension $n$.

revised version, generalized results

References in corpus (3)

• Covariance matrix estimation for stationary time series
• The state space for two qutrits has a phase space structure in its core
• The geometry of bipartite qutrits including bound entanglement