论文标题
Arimoto-rényi条件熵的紧密均匀连续性及其扩展到经典量子状态
A tight uniform continuity bound for the Arimoto-Rényi conditional entropy and its extension to classical-quantum states
论文作者
论文摘要
我们证明，Arimoto版本的条件$α$-Rényi熵的均匀连续性绑定，[0，1）$中的$α\范围。条件性rényi熵的定义是文献中存在的多种形式中最自然的一种，因为它满足了条件熵的两个理想特性，即调节性降低熵的事实，并且不确定性的相关降低不能超过条件获得的信息。此外，它在各种信息理论任务中发现了有趣的应用，例如猜测侧面信息和顺序解码。该条件性熵减少到有条件的香农熵中的限制$α\至1 $，这又使我们能够从结果中恢复后者最近获得的紧密均匀连续性。最后，我们应用结果以获得经典量子状态的条件$α$-Rényi熵的紧密均匀连续性，在与上述同一范围内的$α$以$α$。这再次产生在限制$α\至1 $中的状态条件熵的相应结合。
We prove a tight uniform continuity bound for Arimoto's version of the conditional $α$-Rényi entropy, for the range $α\in [0, 1)$. This definition of the conditional Rényi entropy is the most natural one among the multiple forms which exist in the literature, since it satisfies two desirable properties of a conditional entropy, namely, the fact that conditioning reduces entropy, and that the associated reduction in uncertainty cannot exceed the information gained by conditioning. Furthermore, it has found interesting applications in various information theoretic tasks such as guessing with side information and sequential decoding. This conditional entropy reduces to the conditional Shannon entropy in the limit $α\to 1$, and this in turn allows us to recover the recently obtained tight uniform continuity bound for the latter from our result. Finally, we apply our result to obtain a tight uniform continuity bound for the conditional $α$-Rényi entropy of a classical-quantum state, for $α$ in the same range as above. This again yields the corresponding known bound for the conditional entropy of the state in the limit $α\to 1$.
