AI 中文总结
研究泡利信道上稳定子码的量子通信强逆定理，通过爆破引理证明，当码传输速率高于输入态相干信息时纠缠保真度指数衰减，确定了无记忆信道容量，给出反退化信道情况，还限制了近确定性解码并分离出编码器端陈述。
AI 中文摘要
我们证明了稳定子码类中泡利信道上量子通信的强逆定理。若一个码空间为稳定子群的全联合本征空间的码，其传输速率高于自身输入态的相干信息，则其纠缠保真度随码长指数衰减；编码器可以是到该空间的任意等距映射，解码器可以是任意信道。对于无记忆信道，这确定了每个\(\varepsilon < 1\)时该类的\(\varepsilon\)-量子容量，即容忍恒定误差不会带来速率提升；对于反退化信道，如错误概率\(p \in [1/4, 3/4]\)的去极化信道，其容量为零，而对于\(p \in [1/4,1/2)\)，部分转置界不能证明强逆定理。证明既不使用可加性假设也不使用半定松弛：最优解码恰好在乘积概率空间中的一个事件上成功，所以阿尔斯韦德、加奇斯和科尔纳的爆破引理适用，且其产生的边信息由相干信息承担。该论证还限制了任何类型码的近确定性解码，我们分离出了将其扩展到所有码的编码器端陈述。
英文摘要
We prove a strong converse for quantum communication over Pauli channels within the class of stabilizer codes. If a code whose code space is a full joint eigenspace of a stabilizer group transmits above the coherent information of its own input state, its entanglement fidelity decays exponentially in the block length; the encoder may be any isometry onto that space and the decoder any channel. For memoryless channels this determines the $\varepsilon$-quantum capacity of the class for every $\varepsilon < 1$, so that tolerating a constant error buys no rate; for antidegradable channels, such as the depolarizing channel with error probability $p \in [1/4, 3/4]$, that capacity is zero, while for $p \in [1/4,1/2)$ partial-transposition bounds provably cannot certify a strong converse. The proof uses neither additivity assumptions nor semidefinite relaxations: optimal decoding succeeds precisely on an event in a product probability space, so the blowing-up lemma of Ahlswede, Gács and Körner applies, and the side information it produces is charged against the coherent information. The argument also constrains near-deterministic decoding for codes of any kind, and we isolate the encoder-side statement that would extend it to all of them.
