In this paper, we analyze classical data compression with quantum side information (also known as the classical-quantum Slepian–Wolf protocol) in the so-called large and moderate deviation regimes. In the non-asymptotic setting, the protocol involves compressing classical sequences of finite length $n$ and decoding them with the assistance of quantum side information. In the large deviation regime, the compression rate is fixed, and we obtain bounds on the error exponent function, which characterizes the minimal probability of error as a function of the rate. Devetak and Winter showed that the asymptotic data compression limit for this protocol is given by a conditional entropy. For any protocol with a rate below this quantity, the probability of error converges to one asymptotically and its speed of convergence is given by the strong converse exponent function. We obtain finite blocklength bounds on this function, and determine exactly its asymptotic value. In the moderate deviation regime for the compression rate, the latter is no longer considered to be fixed. It is allowed to depend on the blocklength $n$ , but assumed to decay slowly to the asymptotic data compression limit. Starting from a rate above this limit, we determine the speed of convergence of the error probability to zero and show that it is given in terms of the conditional information variance.

中文翻译：

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具有量子边信息的非渐近经典数据压缩

在本文中，我们在所谓的大偏差和中等偏差范围内分析了具有量子边信息的经典数据压缩（也称为经典量子 Slepian-Wolf 协议）。在非渐近设置中，该协议涉及压缩有限长度 $n$ 的经典序列，并在量子边信息的帮助下对其进行解码。在大偏差状态下，压缩率是固定的，我们获得了误差指数函数的界限，它将误差的最小概率表征为速率的函数。Devetak 和 Winter 表明，该协议的渐近数据压缩限制是由条件熵给出的。对于速率低于此数量的任何协议，误差的概率渐近收敛到1，其收敛速度由强逆指数函数给出。我们获得了这个函数的有限块长度边界，并准确地确定了它的渐近值。在压缩率的中等偏差范围内，后者不再被认为是固定的。允许依赖于块长度 $n$ ，但假设缓慢衰减到渐近数据压缩限制。从高于此限制的速率开始，我们确定错误概率收敛到零的速度，并表明它是根据条件信息方差给出的。后者不再被认为是固定的。允许依赖于块长度 $n$ ，但假设缓慢衰减到渐近数据压缩限制。从高于此限制的速率开始，我们确定错误概率收敛到零的速度，并表明它是根据条件信息方差给出的。后者不再被认为是固定的。允许依赖于块长度 $n$ ，但假设缓慢衰减到渐近数据压缩限制。从高于此限制的速率开始，我们确定错误概率收敛到零的速度，并表明它是根据条件信息方差给出的。