Quantifying continuity of characteristics of composite quantum systems

Abstract

Abstract We describe the most general form of the Alicki–Fannes–Winter method for obtaining uniform continuity bounds for characteristics of composite quantum systems and consider several modifications of this method, which make it applicable to a wide class of characteristics in both finite-dimensional and infinite-dimensional cases. We present uniform continuity bounds for the most important characteristics of composite quantum systems. Along with the results obtained earlier by various authors, we describe a number of new results proved by the proposed methods. In particular, we obtain new continuity bounds for the quantum discord, one-way classical correlation and its regularization in finite-dimensional and infinite-dimensional bipartite quantum systems.