We provide a purely quantum version of polar codes, achieving the symmetric coherent information of any qubit-input quantum channel. Our scheme relies on a recursive channel combining and splitting construction, where a two-qubit gate randomly chosen from the Clifford group is used to combine two single-qubit channels. The inputs to the synthesized bad channels are frozen by preshared EPR pairs between the sender and the receiver, so our scheme is entanglement assisted. We further show that quantum polarization can be achieved by choosing the channel combining Clifford operator randomly, from a much smaller subset of only nine two-qubit Clifford gates. Subsequently, we show that a Pauli channel polarizes if and only if a specific classical channel over a four-symbol input set polarizes. We exploit this equivalence to prove fast polarization for Pauli channels, and to devise an efficient successive cancellation based decoding algorithm for such channels. Finally, we present a code construction based on chaining several quantum polar codes, which is shown to require a rate of preshared entanglement that vanishes asymptotically.

中文翻译：

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使用基于克利福德的通道组合对量子通道进行极化

我们提供了极性代码的纯量子版本，可实现任何量子位输入量子通道的对称相干信息。我们的方案依赖于递归通道合并和拆分构造，其中从Clifford组中随机选择的一个两个量子比特的门用于合并两个单个量子比特的信道。合成不良信道的输入被发送方和接收方之间的预共享EPR对冻结，因此我们的方案得到了纠缠辅助。我们进一步表明，可以通过仅从9个两个量子比特的Clifford门的较小子集中随机选择组合Clifford算子的通道来实现量子极化。随后，我们表明，当且仅当四符号输入集上的特定经典声道发生极化时，保利信道才会极化。我们利用这种等效性来证明Pauli信道的快速极化，并为此类信道设计一种有效的基于连续消除的解码算法。最后，我们提出了一种基于链接几个量子极性代码的代码构造，这表明需要一个渐近消失的预共享纠缠速率。