On Entanglement Breaking Channels for Infinite Dimensional Quantum Systems

The topic of entanglement breaking channels plays an important role in quantum information. Horodecki et al. (Rev. Math. Phys. 15:629–641, 2003) gave a complete characterization of entanglement breaking channels for finite dimensional quantum systems. In the note, we will generalize the results in Horodecki et al. (Rev. Math. Phys. 15:629–641, 2003) to the infinite dimensional case. We first generalized the positive map criterion of the entanglement breaking channel from the finite dimensional case to the infinite dimensional case. As a generalization of entanglement breaking channels for finite dimensional quantum systems, the topic of the strong entanglement breaking channel for arbitrary (finite or infinite) dimensional systems is putted forward. We obtain the operator sum representation of the strong entanglement breaking quantum channel. Applying this operator sum representation, we characterize a category of extreme points of the convex set of all strong entanglement breaking channels, which generalizes corresponding results in the finite dimensional case from Horodecki et al. (Rev. Math. Phys. 15:629–641, 2003).