The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum capacity of most channels is unknown, with wide gaps between the best upper and lower bounds. Even deciding whether a channel has nonzero capacity -- finding its capacity threshold -- is difficult. In this paper we report significant increases in the capacity thresholds of two prototypical noise models: the depolarizing channel and Pauli channels. In the case of the depolarizing channel, this is the first improvement in 18 years, giving a bigger increase beyond the hashing bound than all previous improvements combined. Our starting point is the representation theoretic framework recently proposed by Bhalerao and Leditzky (2025) to compute coherent information for special permutation invariant states. We generalize their framework to the full symmetric subspace, which allow us to optimize coherent information over rank two states in that space. A representation theoretic calculation shows that exponentially many Kraus operators of the channel annihilate the symmetric space, corresponding to a massive decrease in environment entropy for states on the symmetric space compared to the maximally mixed state. This explains the enhanced coherent information as a manifestation of degeneracy for the resulting codes.

翻译：量子容量刻画了量子信道传输量子信息的能力，确立了量子通信的基本极限。尽管在量子信息理论中具有核心地位，多数信道的量子容量仍属未知，最佳上下界之间存在巨大差距。甚至判断信道是否具有非零容量——即确定其容量阈值——也十分困难。本文报告了两种典型噪声模型：退极化信道和泡利信道容量阈值的显著提升。对于退极化信道，这是18年来首次改进，其超越哈希界的增幅超过了此前所有改进的总和。我们的出发点是Bhalerao与Leditzky（2025）近期提出的表示论框架，该框架用于计算特殊置换不变态的相干信息。我们将该框架推广至完全对称子空间，从而能够优化该空间中秩二态上的相干信息。一项表示论计算表明，信道的指数级多个Kraus算符湮灭了对称空间，与最大混合态相比，这对应了对称空间上态的环境熵的大幅降低。这揭示了增强的相干信息是所得码简并性的一种体现。