论文标题
量子差异的某些连续性特性
Some continuity properties of quantum Rényi divergences
论文作者
论文摘要
在二进制量子通道与产品输入之间的歧视问题中，最佳I型I级错误的所有II型误差指数的最高指数零等于Umegaki频道相对熵，而所有类型I类误差指数的最佳指数中，最佳I级错误的最佳指数均与所有夹杂的$ nynyi $ nynyi $ nynyi $ nynyi $ chinds nynyi $ chinds nynyi $ chince nynyi $。我们使用基于夹层rényi脱节的新建立的连续性属性的minimax参数证明了这两个阈值的平等（因此，此问题的强相反属性）。在此激励的情况下，我们对其他各种量子（通道）rényi差异的连续性属性进行了详细的分析，这可能具有独立的兴趣。
In the problem of binary quantum channel discrimination with product inputs, the supremum of all type II error exponents for which the optimal type I errors go to zero is equal to the Umegaki channel relative entropy, while the infimum of all type II error exponents for which the optimal type I errors go to one is equal to the infimum of the sandwiched channel Rényi $α$-divergences over all $α>1$. We prove the equality of these two threshold values (and therefore the strong converse property for this problem) using a minimax argument based on a newly established continuity property of the sandwiched Rényi divergences. Motivated by this, we give a detailed analysis of the continuity properties of various other quantum (channel) Rényi divergences, which may be of independent interest.
