Making good codes for classical-quantum channel coding via quantum hypothesis testing
Making good codes for classical-quantum channel coding via quantum hypothesis testing
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DOI：
10.1109/tit.2007.896874
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发表时间：
2007-06-01
影响因子：
2.5
通讯作者：
Nagaoka, Hiroshi
中科院分区：
文献类型：
--
作者：
Ogawa, Tomohiro;Nagaoka, Hiroshi
在本文中，我们利用量子假设检验的思想，给出了经典量子信道编码定理(Holevo-Schumacher-Westmoland(HSW)定理)直接部分的另一种证明。为了证明良码的存在，我们引用了量子假设检验中与量子斯坦因引理有关的极限定理，作为经典情况下使用的大数定律。我们还使用非对易算子的打包过程来应用好代码的贪婪构造。因此，我们得到了编码错误概率的一个上界，它被用来给出HSW定理的另一种证明。该方法阐明了Holevo信息如何应用于经典量子信道编码问题。
In this correspondence, we give an alternative proof of the direct part of the classical-quantum channel coding theorem (the Holevo-Schumacher-Westmoreland (HSW) theorem), using ideas of quantum hypothesis testing. In order to show the existence of good codes, we invoke a limit theorem, relevant to the quantum Stein's lemma, in quantum hypothesis testing as the law of large numbers used in the classical case. We also apply a greedy construction of good codes using a packing procedure of noncommutative operators. Consequently we derive an upper bound on the coding error probability, which is used to give an alternative proof of the HSW theorem. This approach elucidates how the Holevo information applies to the classical-quantum channel coding problems.