Year: 2021
Type: article
Abstract: We consider a class (convex set) of quantum states containing all finite rank states and infinite rank states with the sufficient rate of decreasing of eigenvalues (in particular, all Gaussian states). Quantum states from this class are characterized by the property (called the FA-property) that allows to obtain several results concerning finite-dimensional approximation of basic entropic and information characteristics of quantum systems and channels. We obtain a simple sufficient condition of the FA-property. We show that all the states with the FA-property form a face of the convex set of all quantum states that is contained within the face of all states with finite von Neumann entropy (the non-coincidence of these two faces follows from the recent result of S. Becker, N. Datta and M.G. Jabbour). We obtain uniform approximation results for characteristics depending on a pair (channel, input state) and for characteristics depending on a pair (channel, input ensemble). We establish the uniform continuity of the above characteristics as functions of a channel w.r.t. the strong convergence provided that the FA-property holds either for the input state or for the average state of input ensemble.
Author: M. E. Shirokov
Institution: Steklov Mathematical Institute
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3138184684