论文标题
几何可区分性措施限制量子通道估计和歧视
Geometric distinguishability measures limit quantum channel estimation and discrimination
论文作者
论文摘要
量子通道估计和歧视是量子信息科学中关注的感兴趣的信息处理任务。在本文中，我们分别采用正确的对数衍生物Fisher信息和几何rényi相对熵来分析这些任务，并且我们还确定了这些可区分性措施之间的联系。我们论文的关键结果是，链条规则的属性可用于正确的对数衍生物Fisher信息和Rényi参数$α$的（0,1）$的间隔$α\ in（0,1）$的几何rényi相对熵。在频道估计中，这些结果意味着海森堡缩放不可识别性的条件，而在渠道歧视中，它们导致了Chernoff和Hoeffding错误指数设置的错误率的提高。更普遍地，我们将摊销的量子渔民信息作为一个概念框架，用于分析估计在量子通道中编码的参数的一般顺序协议，并且除了上述应用程序之外，我们使用该框架来表明当参数在经典 - Quantum通道中编码时不可能进行Heisenberg缩放。然后，我们确定估计和歧视任务与分析每个人的区分性措施之间的许多其他概念和技术联系。作为这项工作的一部分，我们介绍了量子状态和通道的几何相对熵及其特性的详细概述，这可能具有独立的关注。
Quantum channel estimation and discrimination are fundamentally related information processing tasks of interest in quantum information science. In this paper, we analyze these tasks by employing the right logarithmic derivative Fisher information and the geometric Rényi relative entropy, respectively, and we also identify connections between these distinguishability measures. A key result of our paper is that a chain-rule property holds for the right logarithmic derivative Fisher information and the geometric Rényi relative entropy for the interval $α\in(0,1) $ of the Rényi parameter $α$. In channel estimation, these results imply a condition for the unattainability of Heisenberg scaling, while in channel discrimination, they lead to improved bounds on error rates in the Chernoff and Hoeffding error exponent settings. More generally, we introduce the amortized quantum Fisher information as a conceptual framework for analyzing general sequential protocols that estimate a parameter encoded in a quantum channel, and we use this framework, beyond the aforementioned application, to show that Heisenberg scaling is not possible when a parameter is encoded in a classical-quantum channel. We then identify a number of other conceptual and technical connections between the tasks of estimation and discrimination and the distinguishability measures involved in analyzing each. As part of this work, we present a detailed overview of the geometric Rényi relative entropy of quantum states and channels, as well as its properties, which may be of independent interest.
