We consider a quasi-classical version of the Alicki-Fannes-Winter technique widely used for quantitative continuity analysis of characteristics of quantum systems and channels. This version allows us to obtain continuity bounds under constraints of different types for quantum states belonging to subsets of a special form that can be called "quasi-classical". Several applications of the proposed method are described. Among others, we obtain the universal continuity bound for the von Neumann entropy under the energy-type constraint which in the case of one-mode quantum oscillator is close to the specialized optimal continuity bound presented recently by Becker, Datta and Jabbour. We obtain semi-continuity bounds for the quantum conditional entropy of quantum-classical states and for the entanglement of formation in bipartite quantum systems with the rank/energy constraint imposed only on one state. Semi-continuity bounds for entropic characteristics of classical random variables and classical states of a multi-mode quantum oscillator are also obtained.

翻译：本文考虑Alicki-Fannes-Winter技巧的一种准经典版本，该技巧广泛用于量子系统与通道特性的定量连续性分析。此版本允许我们在不同类型约束条件下，对属于可称为"准经典"特殊形式子集的量子态建立连续性界。文中描述了所提出方法的若干应用。其中，我们得到了能量型约束下冯·诺依曼熵的普适连续性界——在单模量子振子情形下，该结果接近Becker、Datta与Jabbour近期提出的专用最优连续性界。我们获得了量子-经典态量子条件熵以及秩/能量约束仅施加于一个状态的二分量子系统纠缠形成度的半连续性界。此外，还得到了经典随机变量与多模量子振子经典态的熵特征量半连续性界。