将信道极化同时应用于 amplitude 与 phase 合成信道，以递归编码和 coherent successive-cancellation 实现量子通信码。
聚焦量子信道编码与渐近率，不与实验 QEC memory code 或经典 polar code 混同。
code/channel/quantum-polarCode dossier
这里汇总参数景观中的结构化记录、码族谱系中的构造说明、执行路线与外部知识库，作为完整主题页的代码专属延伸。
k、冻结集合与有限长度性能由目标量子信道决定，不能给一个脱离信道的固定 [[n,k,d]]。
同时极化 amplitude 与 phase synthesized channels。
同时极化 amplitude 与 phase synthesized channels。
amplitude/phase channels
successive cancellation
coherent-information rate
聚焦量子信道编码与渐近率，不与实验 QEC memory code 或经典 polar code 混同。
Quantum Polar Channel-code Execution Route：信道极化、振幅/相位合成信道、冻结集合、相干逐次消除与有限长度评测。当前路线绑定 Coherent successive-cancellation、Channel-mismatched polar decoder，并覆盖 Amplitude synthesized-channel observations、Phase synthesized-channel observations。
k、冻结集合与有限长度性能由目标量子信道决定，不能给一个脱离信道的固定 [[n,k,d]]。
容量可达是信道渐近结论，不等于门噪声容错；有限实例必须绑定设计信道、可靠索引集合和纠缠辅助消耗。
2015Efficient Quantum Polar Codes Requiring No Preshared Entanglement2012Quantum polar codes for arbitrary channelsDeep reference
定义、代数构造、保护能力与执行证据均按来源段落独立维护；中文稿经过术语整理，英文稿保留用于逐段对照。
量子 Polar 码把 Arıkan 信道极化同时用于互补的振幅与相位信息，选择对两者都可靠的合成信道承载量子数据。构造是信道依赖的 CSS 编码，其可达率与量子信道的 coherent information 相关。
Quantum polar codes apply Arikan channel polarization to complementary amplitude and phase information, placing quantum data on synthesized channels reliable for both. The result is a channel-dependent CSS construction with achievable rate related to the channel coherent information.
长度 N=2^m 的 polar 变换递归组合信道；索引按振幅可靠性和相位可靠性分成信息、冻结、纠缠辅助等集合。生成矩阵、bit-reversal 约定、冻结值与信道参数共同确定实例。
For length N=2^m, the polar transform recursively combines channels. Indices are partitioned by amplitude and phase reliability into information, frozen, and possibly entanglement-assisted sets; generator matrix, bit-reversal convention, frozen values, and channel parameters define the instance.
保护针对给定量子信道的随机错误概率，而不是以最坏情况 Pauli 重量为唯一指标。有限长度性能取决于振幅/相位合成信道的可靠性估计，可能没有简单可用的单一距离 d。
Protection is tailored to stochastic errors of a specified quantum channel rather than solely to worst-case Pauli weight. Finite-length performance depends on reliability estimates for amplitude and phase synthesized channels and may not be summarized by one useful distance d.
块长为 2 的幂，逻辑数由同时可靠索引的数量减去资源集合后得到。应报告设计信道、块长、信息集合、冻结集合、ebit 消耗以及有限长度误码率，而不只给渐近容量。
Block length is a power of two and the logical count follows from indices reliable in both bases after resource sets are assigned. Report design channel, block length, information and frozen sets, ebit consumption, and finite-length error, not only asymptotic capacity.
Polar 编码网络主要由 CNOT 类线性变换组成，适合递归编译，但这不意味着逻辑门具有横向通用性。它首先是通信编码；用于容错计算需另行构造逻辑门与综合征协议。
The polar encoder is mainly a recursive network of CNOT-like linear transforms, but this does not imply a universal transversal logical gate set. It is primarily a communication code; fault-tolerant computation requires separate logical-gate and syndrome protocols.
量子 successive-cancellation 解码先恢复振幅信息，再利用带侧信息的相位解码；也可表述为张量网络收缩。有限长度实现需要可靠性构造、软信道输出和误差传播管理。
Quantum successive-cancellation decoding recovers amplitude information and then phase information with side information, and can also be viewed as tensor-network contraction. Finite-length implementations need reliability construction, soft channel outputs, and error-propagation control.
容量可达性并不等于门噪声下容错。编码/解码深度、长程 CNOT 路由、冻结量子比特制备和中间测量故障都需加入线路模型；纠缠辅助集合也必须有物理来源。
Capacity achievement is not fault tolerance under gate noise. Encoder depth, long-range CNOT routing, frozen-qubit preparation, and measurement faults need a circuit model, and any entanglement-assisted set needs a physical supply.
有限长度实验可在模拟信道或小型处理器上实现 polar 编码网络并比较块错误率。可扩展性瓶颈常在路由、可靠性构造和 coherent successive cancellation，而不是矩阵存储。
Finite-length experiments can implement the polar encoder on simulated channels or small processors and compare block error. Scaling bottlenecks often lie in routing, reliability construction, and coherent successive cancellation rather than matrix storage.
量子 Polar 码与经典 polar 码共享递归变换，并通过 CSS 互补观测联系量子信道编码。某些退化信道上纠缠辅助率可消失，但不能把这一条件推广到任意信道。
Quantum polar codes share the recursive transform with classical polar codes and connect to quantum channel coding through complementary CSS observables. Entanglement assistance can vanish for certain channel classes, but that condition is not universal.
“Polar 码”实例必须绑定设计信道；同一 N、k 在不同退极化率或擦除率下会选择不同索引。数据库精确映射需比较索引集合或生成网络，而非只比 [[N,k]].
A polar-code instance must be tied to its design channel: equal N and k can select different indices at different depolarizing or erasure rates. Exact database mapping requires the index sets or encoder network, not only [[N,k]].