从雷尼熵权到量子态的信息扫描
From Rényi Entropy Power to Information Scan of Quantum States
摘要：
在估计理论的背景下，我们推广的概念香农的熵功率的雷尼熵设置。这不仅允许发现新的估计不等式，例如基于Rényi熵的De Bruijn恒等式，等周不等式或Stam不等式，而且还为推导基于Rényi熵幂的单参数量子力学不确定关系族提供了一个方便的技术框架。为了让更多的肉在骨头上，我们使用获得的雷尼熵功率来展示与量子态相关的信息概率分布如何在类似于量子态断层扫描的过程中重建。我们用所谓的“猫态”来说明这一点的内部工作原理，猫态在量子精密测量等方案中具有根本意义和实际用途。突出的问题，包括扩展的概念熵功率Tsallis熵和随后的影响估计理论也进行了简要讨论。
英文摘要：
In the estimation theory context, we generalize the notion of Shannon's entropy power to the Rényi-entropy setting. This not only allows to find new estimation inequalities, such as the Rényi-entropy based De Bruijn identity, isoperimetric inequality or Stam inequality, but it also provides a convenient technical framework for the derivation of a one-parameter family of Rényi-entropy-power-based quantum-mechanical uncertainty relations. To put more flesh on the bones, we use the Rényi entropy power obtained to show how the information probability distribution associated with a quantum state can be reconstructed in a process that is akin to quantum-state tomography. We illustrate the inner workings of this with the so-called "cat states", which are of fundamental interest and practical use in schemes such as quantum metrology. Salient issues, including the extension of the notion of entropy power to Tsallis entropy and ensuing implications in estimation theory are also briefly discussed.
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