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Non-Asymptotic Classical Data Compression With Quantum Side Information

机译：具有量子侧信息的非渐近古典数据压缩

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摘要

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.
机译：在本文中，我们在所谓的大型和中等偏差方案中分析具有量子侧信息（也称为经典绞线 - 狼协议）的古典数据压缩。在非渐近设置中，协议涉及压缩有限长度的经典序列<内联公式XMLNS：mml =“http://www.w3.org/1998/math/mathml”xmlns：xlink =“http：// www.w3.org/1999/xlink“> $ n $ 并在量子侧信息的帮助下解码它们。在大的偏差方案中，压缩率是固定的，并且我们在错误指数函数上获得界限，其特征在于速率的误差概率最小概率。德弗拉克和冬季表明，该协议的渐近数据压缩极限由条件熵给出。对于低于此数量速率的任何协议，误差会聚到一个渐近的概率并通过强的逆转指数函数给出其收敛速度。我们在此功能上获得有限的块长度界限，并确定其渐近值。在压缩率的中等偏差方案中，后者不再被认为是固定的。允许依赖于BlockLength <内联公式XMLNS：MML =“http://www.w3.org/1998/math/mathml”xmlns：xlink =“http://www.w3.org/1999/1999/ xlink“> $ n $ ，但假设慢慢衰减到渐近数据压缩限制。从高于此限制的速率开始，我们确定误差概率的收敛速度为零，并表明它在条件信息方差方面给出。

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