We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an $n$-partite system $A = (A_1, \ldots A_n)$ corresponds to the sum of the entropies of its parts $A_i$. The Asymptotic Equipartition Property implies that this is indeed the case to first order in $n$, under the assumption that the parts $A_i$ are identical and independent of each other. Here we show that entropy accumulation occurs more generally, i.e., without an independence assumption, provided one quantifies the uncertainty about the individual systems $A_i$ by the von Neumann entropy of suitably chosen conditional states. The analysis of a large system can hence be reduced to the study of its parts. This is relevant for applications. In device-independent cryptography, for instance, the approach yields essentially optimal security bounds valid for general attacks, as shown by Arnon-Friedman et al.

中文翻译：

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熵累积

我们问熵是否累积的问题，因为关于 $n$-partite 系统 $A = (A_1, \ldots A_n)$ 的操作相关总不确定性对应于其部分 $A_i$ 的熵总和。渐近均分性质意味着这确实是 $n$ 中一阶的情况，假设 $A_i$ 部分相同且彼此独立。Here we show that entropy accumulation occurs more generally, ie, without an independence assumption, provided one quantifies the uncertainty about the individual systems $A_i$ by the von Neumann entropy of suitably chosen conditional states. 因此，对大型系统的分析可以简化为对其各部分的研究。这与应用程序相关。例如，在独立于设备的密码学中，