标题： 通过凸优化定义量子散度 显示英文标题

标题： Defining quantum divergences via convex optimization

摘要： 我们引入了一种新的量子Rényi散度$D^{\#}_{\alpha}$，它对于$\alpha \in (1,\infty)$的定义是通过一个凸优化程序来实现的。 这种散度具有若干理想的计算和操作性质，例如对状态和通道的有效半定规划表示，以及链式规则性质。 这种新散度的一个重要性质是，其正则化等于夹心（也称为最小）量子Rényi散度。 这使我们能够证明几个结果。 首先，我们利用它来得到关于量子通道之间的正则化夹心$\alpha$-Rényi散度的收敛层次上界，针对$\alpha > 1$。 其次，它允许我们证明夹心$\alpha$-Rényi散度对于$\alpha > 1$的链式规则性质，我们利用它来表征通道区分的强逆指数。 最后，它使我们能够获得量子通道容量的改进界限。 显示英文摘要

摘要： We introduce a new quantum R\'enyi divergence $D^{\#}_{\alpha}$ for $\alpha \in (1,\infty)$ defined in terms of a convex optimization program. This divergence has several desirable computational and operational properties such as an efficient semidefinite programming representation for states and channels, and a chain rule property. An important property of this new divergence is that its regularization is equal to the sandwiched (also known as the minimal) quantum R\'enyi divergence. This allows us to prove several results. First, we use it to get a converging hierarchy of upper bounds on the regularized sandwiched $\alpha$-R\'enyi divergence between quantum channels for $\alpha > 1$. Second it allows us to prove a chain rule property for the sandwiched $\alpha$-R\'enyi divergence for $\alpha > 1$ which we use to characterize the strong converse exponent for channel discrimination. Finally it allows us to get improved bounds on quantum channel capacities.