On the Duality Between the BSC and Quantum PSC
On the Duality Between the BSC and Quantum PSC
复制标题
论BSC与量子PSC之间的对偶性
DOI：
10.1109/isit45174.2021.9518034
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Pfister, Henry D.
中科院分区：
文献类型：
--
作者：
Rengaswamy, Narayanan;Pfister, Henry D.
在2018年，Renes [IEEE Trans. Inf. Theory，第64卷，第1期，第111页]。577-592（2018）]发展了经典输入量子输出通道的通道对偶性的一般理论。他的结果表明，一些著名的二元擦除信道上的线性码的对偶性结果可以扩展到一般的经典信道，但代价是使用本质上是量子力学的对偶问题。这种对偶性的一个特殊情况是量子纯态信道（PSC）上的纠错编码和经典二进制对称信道（BSC）上的窃听保密编码之间的联系。类似地，BSC上的纠错编码与PSC上的窃听保密有关。虽然这一结果对经典编码有重要意义，但对于没有强大量子信息理论背景的研究人员来说，一般对偶结果背后的机制是相当具有挑战性的。在这项工作中，我们利用先前的结果对PSC的线性码给出了一个替代推导上述特殊情况下，通过计算性能指标的封闭形式的表达式。已有的结果包括PSC上线性码的平方根度量的最优性和线性码的傅立叶对偶性。
In 2018, Renes [IEEE Trans. Inf. Theory, vol. 64, no. 1, pp. 577-592 (2018)] developed a general theory of channel duality for classical-input quantum-output channels. His result shows that a number of well-known duality results for linear codes on the binary erasure channel can be extended to general classical channels at the expense of using dual problems which are intrinsically quantum mechanical. One special case of this duality is a connection between coding for error correction on the quantum pure-state channel (PSC) and coding for wiretap secrecy on the classical binary symmetric channel (BSC). Similarly, coding for error correction on the BSC is related to wire-tap secrecy on the PSC. While this result has important implications for classical coding, the machinery behind the general duality result is rather challenging for researchers without a strong background in quantum information theory. In this work, we leverage prior results for linear codes on PSCs to give an alternate derivation of the aforementioned special case by computing closed-form expressions for the performance metrics. The noted prior results include the optimality of square-root measurement for linear codes on the PSC and the Fourier duality of linear codes.