Institut für Theoretische Physik, ETH Zurich, Switzerland.
Phys Rev Lett. 2012 Aug 3;109(5):050504. doi: 10.1103/PhysRevLett.109.050504. Epub 2012 Aug 1.
Polar coding, introduced 2008 by Arıkan, is the first (very) efficiently encodable and decodable coding scheme whose information transmission rate provably achieves the Shannon bound for classical discrete memoryless channels in the asymptotic limit of large block sizes. Here, we study the use of polar codes for the transmission of quantum information. Focusing on the case of qubit Pauli channels and qubit erasure channels, we use classical polar codes to construct a coding scheme that asymptotically achieves a net transmission rate equal to the coherent information using efficient encoding and decoding operations and code construction. Our codes generally require preshared entanglement between sender and receiver, but for channels with a sufficiently low noise level we demonstrate that the rate of preshared entanglement required is zero.
极化码由阿里坎于 2008 年提出，是第一个（非常）高效可编码和解码的编码方案，其信息传输速率在大的块大小的渐近极限下，可证明达到经典离散无记忆信道的香农极限。在这里，我们研究了极化码在量子信息传输中的应用。聚焦于量子比特 Pauli 信道和量子比特删除信道的情况，我们使用经典极化码构建了一种编码方案，该方案通过高效的编码和解码操作和码构造，在渐近情况下实现了等于相干信息的净传输速率。我们的码通常需要发送方和接收方之间预先共享纠缠，但对于噪声水平足够低的信道，我们证明所需的预先共享纠缠的速率为零。
