In this talk I will consider the (convex) stability property of the set of quantum states and its stronger version, providing useful tools in study of infinite dimensional quantum systems. I will briefly describe applications of the stability property to analysis of continuity of the important characteristics related to the classical capacity of a quantum channel and to the notion of entanglement of a state of a composite system.

The stronger version of stability makes possible to develop the special approximation approach to study of concave (convex) functions on the set of quantum states, which can be applied to many characteristics used in the quantum information theory (the von Neumann entropy, the output entropy of a quantum channel, the mutual information, etc.).

Paper reference: arXiv:0804.1515, arXiv:0904.1963