论文标题
强烈的匡威边界以压缩混合状态
Strong Converse Bounds for Compression of Mixed States
论文作者
论文摘要
在本文中，我们研究了混合状态的可见和盲区压缩的强相反特性。可见的压缩方案的最佳速率是根据纯化的纠缠而获得的，到目前为止，其添加性仍然未知。对于扩展状态的变化，我们证明了纯化的纠缠是加性的，并将其应用于获得“相当强”的匡威束缚，以构成这种状态的盲目和可见的压缩。也就是说，当速率降低到最佳速率以下时，错误表现出不连续的跳跃从0到$ \ frac {1} {3 \ sqrt {2}} $。 要处理一般状态的可见案例，我们定义了一个新数量$ e_ {α，p}（a：r）_ρ$用于双分部分状态$ρ^{ar} $和$α\ in（0,1）\ cup（1，\ infty）$作为$α$-rényi$ nynyi nyi nyi $ $ e $ e $ e $ e的cup（1，\ infty）$。对于$α= 1 $，我们定义$ e_ {1，p}（a：r）_ρ：= e_ {p}（a：r）_ρ$。我们表明，以低于正则化的任何速率$ \ lim_ {α\至1^+} \ frac {e_ {α，p}（a^n：r^n）_ {ρ^{\ otimes n}}}}}} {n} {n} $可见的压缩的保真度指数呈呈成正力收敛到零。 此外，我们考虑了一般混合国家来源的盲压缩$ρ^{ar} $共享编码器和不可访问的参考系统$ r $之间的盲。我们通过假设解码器是一个超积极通道，从而获得了对该源压缩的强逆向束缚。这立即暗示着通过假设超积极解码器对混合状态集合的盲目压缩的强烈交谈，因为这是一般混合国家源$ρ^{ar} $的特殊情况，其中参考系统$ r $具有经典结构。
In this paper, we study strong converse properties for both visible and blind compression of mixed states. The optimal rate of a visible compression scheme is obtained in terms of the entanglement of purification, whose additivity remains unknown so far. For a variation of extendible states, we prove that the entanglement of purification is additive and apply this to obtain a "pretty strong" converse bound for the blind and visible compression of such states. Namely, when the rate decreases below the optimal rate, the error exhibits a discontinuous jump from 0 to at least $\frac{1}{3\sqrt{2}}$. To deal with the visible case for general states, we define a new quantity $E_{α,p}(A:R)_ρ$ for a bipartite state $ρ^{AR}$ and $α\in (0,1)\cup (1,\infty)$ as the $α$-Rényi generalization of the entanglement of purification $E_{p}(A:R)_ρ$. For $α=1$, we define $E_{1,p}(A:R)_ρ:=E_{p}(A:R)_ρ$. We show that for any rate below the regularization $\lim_{α\to 1^+}E_{α,p}^{\infty}(A:R)_ρ:=\lim_{α\to 1^+} \lim_{n \to \infty} \frac{E_{α,p}(A^n:R^n)_{ρ^{\otimes n}}}{n}$ the fidelity for the visible compression exponentially converges to zero. Moreover, we consider blind compression of a general mixed-state source $ρ^{AR}$ shared between an encoder and an inaccessible reference system $R$. We obtain a strong converse bound for the compression of this source by assuming that the decoder is a super-unital channel. This immediately implies a strong converse for the blind compression of ensembles of mixed states, by assuming a super-unital decoder, as this is a special case of the general mixed-state source $ρ^{AR}$ where the reference system $R$ has a classical structure.
