A well-known result due to Fannes is a certain upper bound on the modulus of continuity of the von Neumann entropy with respect to the trace distance between density matrices; this distance is the maximum probability of distinguishing between the corresponding quantum states. Much more recently, Audenaert obtained an exact expression of this modulus of continuity. In the present note, Audenaert's result is extended to a broad class of entropy functions indexed by arbitrary continuous convex functions $f$ in place of the Shannon--von Neumann function $x\mapsto x\log_2x$. The proof is based on the Schur majorization.

翻译：由范恩斯引起的一个众所周知的结果是,在密度矩阵之间的痕量距离方面,冯纽曼entropy的连续性模量具有一定的上限;这一距离是区分相应量子状态的最大可能性。最近,奥德纳特获得了这种连续性模量的确切表达。在本说明中,奥德纳特的结果扩大到以任意连续convex函数指数化的一大类对流函数,取代香农-von Neumann函数 $x\mapsto xlog_2x$。证据基于Schur的占多数。