论文标题
具有量子侧信息的数据压缩的可实现的错误指数和对称古典量子通道的通信
Achievable error exponents of data compression with quantum side information and communication over symmetric classical-quantum channels
论文作者
论文摘要
香农理论（经典或量子）的基本兴趣是给定信道W和速率r的最佳错误指数：常数e（w，r），它在使用较大的固定速率r的较大固定速率r的指数衰减中，以越来越多的固定速率r来进行较大的固定代码，以越来越多地传达给定通道的无数（内存）。隐私放大中的数量意味着在对称的经典量词通道上通信的误差指数上的下限。最终的界限与达赖的[IEEE TIT 59，8027（2013）]相匹配，以高于临界值的速率，并重现了对称通道的众所周知的经典结果。该参数首先将隐私放大的误差指数与带有量子侧信息压缩的经典信息的误差指数，这给出了与Cheng等人的球形包装上限相匹配的下限。 [IEEE TIT 67，902（2021）]。反过来，Cheng等人发现的多项式预成分对球形包装的结合。可以将Li，Yao和Hayashi [Arxiv：2111.01075 [QUANT-PH]]提升为隐私放大问题，至少用于线性随机性提取器。
A fundamental quantity of interest in Shannon theory, classical or quantum, is the optimal error exponent of a given channel W and rate R: the constant E(W,R) which governs the exponential decay of decoding error when using ever larger codes of fixed rate R to communicate over ever more (memoryless) instances of a given channel W. Here I show that a bound by Hayashi [CMP 333, 335 (2015)] for an analogous quantity in privacy amplification implies a lower bound on the error exponent of communication over symmetric classical-quantum channels. The resulting bound matches Dalai's [IEEE TIT 59, 8027 (2013)] sphere-packing upper bound for rates above a critical value, and reproduces the well-known classical result for symmetric channels. The argument proceeds by first relating the error exponent of privacy amplification to that of compression of classical information with quantum side information, which gives a lower bound that matches the sphere-packing upper bound of Cheng et al. [IEEE TIT 67, 902 (2021)]. In turn, the polynomial prefactors to the sphere-packing bound found by Cheng et al. may be translated to the privacy amplification problem, sharpening a recent result by Li, Yao, and Hayashi [arXiv:2111.01075 [quant-ph]], at least for linear randomness extractors.
