利用编码端与解码端预共享的 ebits 放宽稳定子校验的对易约束，从更广泛的经典线性码构造量子码。
记录 entanglement consumption 与净通信率；不把预共享纠缠成本隐藏在普通 stabilizer-code 参数中。
code/assisted/entanglement-assistedCode 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。
额外资源 c 改变载体与检查定义，不能在不显示 ebit 的普通 [[n,k,d]] 图中直接比较。
发送端四个噪声量子比特加接收端一半预共享 ebit。
发送端四个噪声量子比特加接收端一半预共享 ebit。
shared ebits
relaxed dual-containing constraint
catalytic variants
记录 entanglement consumption 与净通信率；不把预共享纠缠成本隐藏在普通 stabilizer-code 参数中。
Entanglement-assisted QECC Channel Execution Route：预共享 ebit、发送端编码、噪声信道、扩展 syndrome、接收端恢复与净资源评测。当前路线绑定 EA stabilizer syndrome decoder、Channel-aware maximum-likelihood decoder，并覆盖 Entanglement-assisted stabilizer extraction、Receiver-ebit joint syndrome。
额外资源 c 改变载体与检查定义，不能在不显示 ebit 的普通 [[n,k,d]] 图中直接比较。
分号后的 c 是不可省略的资源维度；若接收端 ebit 半部有噪声，标准 [[n,k,d;c]] 纠错保证必须重新分析。
2006Correcting quantum errors with entanglementDeep 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。
纠缠辅助量子纠错码允许发送方与接收方预共享 c 对 ebit，从而放宽标准稳定子检查的辛正交约束，参数写作 [[n,k,d;c]]。接收方的 ebit 半部通常假定不经过噪声信道。
Entanglement-assisted quantum error-correcting codes consume c preshared ebits between sender and receiver, relaxing the symplectic-orthogonality constraint of ordinary stabilizer checks. Parameters are written [[n,k,d;c]], with receiver halves conventionally assumed noiseless.
从任意经典二元或四元校验矩阵构造时，不对易检查的辛 Gram 矩阵秩决定所需 ebit 数。扩展稳定子作用在发送方 n 个信道量子比特与接收方 c 个参考半部上，恢复整体对易性。
Starting from arbitrary binary or quaternary checks, the rank of their symplectic Gram matrix determines the required ebits. The enlarged stabilizer acts on n transmitted qubits and c receiver reference halves, restoring commutativity.
距离 d 仍由作用在发送方噪声载体上的最小非平凡逻辑误差决定，可纠正至多 floor((d−1)/2) 个任意发送方量子比特错误。若接收方半部也有噪声，必须改用带噪纠缠辅助模型。
Distance d is still set by the minimum nontrivial logical error on the sender's noisy carriers, correcting up to floor((d-1)/2) arbitrary sender-qubit errors. If receiver halves are noisy, a noisy-entanglement-assisted model is required.
必须同时报告发送码率 k/n、纠缠消耗 c/n，以及在所选通信任务中的净率约定。省略 c 会把不同资源模型的码错误地放在同一参数景观中。
Report transmitted rate k/n, entanglement consumption c/n, and the chosen net-rate convention for the communication task. Omitting c incorrectly merges codes that use different resource models.
逻辑操作可以利用发送块上的稳定子结构与接收端已有纠缠，但预共享 ebit 本身不保证横向门或通用性。通信协议还要说明 ebit 建立、验证和消耗是否计入成本。
Logical operations may exploit the sender stabilizer structure and preshared entanglement, but ebits alone guarantee neither transversality nor universality. A communication protocol must state whether ebit creation, verification, and consumption count toward cost.
接收方联合测量到达的 n 个量子比特与本地 ebit 半部，所得综合征可用稳定子查表、最小权或基于信道似然的解码。编码矩阵若源自非自正交经典码，解码器必须保留对应辛结构。
The receiver jointly measures the n received qubits and local ebit halves, then decodes the syndrome by lookup, minimum weight, or channel likelihood. When checks come from a non-self-orthogonal classical code, the decoder must retain the corresponding symplectic structure.
通信纠错能力与计算容错是两层问题。若要重复使用协议或实现逻辑门，必须分析 ebit 制备故障、接收端存储错误、综合征电路与经典反馈；理想 ebit 假设应显式标注。
Communication correction and computational fault tolerance are separate layers. Repeated use or logical gates require analysis of ebit-preparation faults, receiver memory, syndrome circuits, and feedback, with the ideal-ebit assumption stated explicitly.
实验可通过先制备 Bell 对、保留一半并让另一半随编码块通过噪声通道来验证优势。公平基线应计入纠缠分发保真度、存储时间与额外量子比特。
An experiment can prepare Bell pairs, retain one half, and send the other with the encoded block through a noisy channel. A fair baseline includes entanglement-distribution fidelity, storage time, and extra qubits.
EAQECC 将普通稳定子码推广到非自正交经典输入；c=0 时退化为标准稳定子情形。它也与量子通信中的 father protocol 和纠缠辅助容量相关，但不应与纠缠净化协议简单等同。
EAQECC generalizes ordinary stabilizer coding to non-self-orthogonal classical inputs and reduces to the standard case at c=0. It relates to entanglement-assisted communication protocols and capacities but is not simply an entanglement-purification protocol.
看到 [[n,k,d]] 相同不能忽略分号后的 c。外部数据库若不支持 ebit 字段，应把记录标为资源模型不完整，而不是把 c 填入稳定子数或 gauge 数。
Equal [[n,k,d]] does not justify dropping c after the semicolon. If an external database lacks an ebit field, mark the resource model incomplete rather than place c in a stabilizer or gauge count.