On Quantum States with a Finite-Dimensional Approximation Property

We consider a class (convex set) of quantum states containing all finite rank and infinite with the sufficient rate decreasing eigenvalues (in particular, Gaussian states). Quantum from this are characterized by property (called FA-property) that allows to obtain several results concerning finite-dimensional approximation basic entropic information characteristics systems channels. simple condition FA-property. show implies finiteness von Neumann entropy, but leave unsolved question converse implication. uniform for depending on pair (channel, input state) ensemble). establish continuity above as functions channel w.r.t. strong convergence provided FA-property holds either state or average ensemble.