基于向量值$L_p$范数的相关性度量
A Correlation Measure Based on Vector-Valued $L_p$-Norms
摘要：
本文引入了一种新的二体量子态关联测度。该度量依赖于参数$α$，并且根据向量值$L_p$ -范数来定义。该度量在$α$互信息的指数的常数内，并且减少到$α=1$的迹范数（总变差距离）。我们将证明一些解耦型定理在这种措施的相关性，并提出了一些应用在隐私放大以及在绑定的随机编码指数。特别地，我们根据\emph{Csiszár's proposal}建立了关于$α$互信息的窃听信道的保密指数的界（在总变差度量下）。
英文摘要：
In this paper, we introduce a new measure of correlation for bipartite quantum states. This measure depends on a parameter $α$, and is defined in terms of vector-valued $L_p$-norms. The measure is within a constant of the exponential of $α$-Rényi mutual information, and reduces to the trace norm (total variation distance) for $α=1$. We will prove some decoupling type theorems in terms of this measure of correlation, and present some applications in privacy amplification as well as in bounding the random coding exponents. In particular, we establish a bound on the secrecy exponent of the wiretap channel (under the total variation metric) in terms of the $α$-Rényi mutual information according to \emph{Csiszár's proposal}.
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