The Schmidt number and partially entanglement breaking channels in infinite dimensions

Understand

A definition of the Schmidt number of a state of an infinite dimensional bipartite quantum system is given and properties of the corresponding family of Schmidt classes are considered.

• The existence of states with a given Schmidt number such that any their countable convex decomposition does not contain pure states with finite Schmidt rank is established.
• Partially entanglement breaking channels in infinite dimensions are studied.
• Several properties of these channels well known in finite dimensions are generalized to the infinite dimensional case.