论文标题
通过凸优化定义量子差异
Defining quantum divergences via convex optimization
论文作者
论文摘要
我们引入了一个新的量子rényidivergence $ d^{\＃}_α$，for $α\ in（1，\ infty）$根据凸优化程序定义。这种差异具有几个理想的计算和操作属性，例如针对状态和渠道的有效的半决赛编程表示以及链条规则属性。这种新差异的重要特性是其正则化等于夹杂的（也称为最小）量子rényi差异。这使我们能够证明几个结果。首先，我们使用它在量子通道之间的正规化夹心$α$-Rényi差异上获得上限的融合层次结构，价格为$α> 1 $。其次，它使我们能够证明夹杂的$α$-RényiDivergence $α> 1 $的链条规则属性，我们用来表征强烈的匡威指数用于频道歧视。最后，它使我们能够在量子通道容量上获得改进的界限。
We introduce a new quantum Rényi divergence $D^{\#}_α$ for $α\in (1,\infty)$ 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 Rényi divergence. This allows us to prove several results. First, we use it to get a converging hierarchy of upper bounds on the regularized sandwiched $α$-Rényi divergence between quantum channels for $α> 1$. Second it allows us to prove a chain rule property for the sandwiched $α$-Rényi divergence for $α> 1$ which we use to characterize the strong converse exponent for channel discrimination. Finally it allows us to get improved bounds on quantum channel capacities.
