经典量子极化码的高效译码
Towards efficient decoding of classical-quantum polar codes
摘要：
用于在具有经典输入和量子输出的一般信道（cq信道）上以容量速率发送比特的已知策略需要解码器实现不切实际的复杂的集体测量。在这里，我们表明，一个完全集体的战略是没有必要的，以恢复所有的信息位。事实上，当编码用于cq信道W的大量N次使用时，可以通过非集体策略来恢复N I（W_acc）比特，该非集体策略相当于对乘积测量的结果进行相干量子处理，其中I（W_acc）是信道W的可访问信息。为了解码其他N（I（W）- I（W_acc））个比特，其中I（W）是Holevo速率，我们的结论是接收机应该采用集体测量。我们还提出了另外两个结果：1）集体Fuchs-Caves测量（量子似然比测量）可以在接收器处使用以实现Holevo速率; 2）我们给出了用于小尺寸极化码的Helstrom测量的显式形式。用于证明这些结果的主要方法是Arikan极化码的量子扩展。
英文摘要：
Known strategies for sending bits at the capacity rate over a general channel with classical input and quantum output (a cq channel) require the decoder to implement impractically complicated collective measurements. Here, we show that a fully collective strategy is not necessary in order to recover all of the information bits. In fact, when coding for a large number N uses of a cq channel W, N I(W_acc) of the bits can be recovered by a non-collective strategy which amounts to coherent quantum processing of the results of product measurements, where I(W_acc) is the accessible information of the channel W. In order to decode the other N (I(W) - I(W_acc)) bits, where I(W) is the Holevo rate, our conclusion is that the receiver should employ collective measurements. We also present two other results: 1) collective Fuchs-Caves measurements (quantum likelihood ratio measurements) can be used at the receiver to achieve the Holevo rate and 2) we give an explicit form of the Helstrom measurements used in small-size polar codes. The main approach used to demonstrate these results is a quantum extension of Arikan's polar codes.
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