尖锐的量子容量阈值：可降和不可降信道的指数强逆
Sharp Quantum Capacity Thresholds: Exponential Strong Converses for Degradable and Antidegradable Channels
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中文总结 AI 辅助
本文证明有限维可降和不可降信道存在指数强逆，确立量子删除信道全参数范围的首个全码指数强逆，还得到适用于一般有限维信道的可计算界。
中文摘要 AI 辅助
噪声信道的量子容量量化了可可靠传输量子信息的最大速率。对于一般信道，其评估需对任意多信道使用次数进行优化；可降信道是核心例外，其容量由单字母相干信息给出，而不可降信道容量为零。不过，即使对这些基础类别，当容忍固定非最大误差时，通信是否可在容量以上进行仍悬而未决。本文通过证明所有有限维可降和不可降信道的指数强逆解决了该问题：在任何高于容量的速率下，所有编码方案的保真度随信道使用次数呈指数衰减。作为直接结果，我们确立了量子删除信道在全参数范围内的首个全码指数强逆，强化了此前仅适用于几乎所有码的结果。我们还证明指数强逆界在接收机后处理下保持不变，这为任意有限维信道产生了可高效计算的半定规划界，为泡利信道提供了改进的界，并为一类不可降多能级振幅阻尼信道给出了精确的指数强逆。
英文摘要
The quantum capacity of a noisy channel quantifies the maximum rate at which quantum information can be transmitted reliably. For general channels, its evaluation requires an optimization over arbitrarily many channel uses. Degradable channels form a central exception: their capacity is given by the single-letter coherent information, while antidegradable channels have zero capacity. Nevertheless, even for these fundamental classes, it has remained open whether communication above capacity becomes possible when a fixed non-maximal error is tolerated. Here we resolve this problem by proving an exponential strong converse for every finite-dimensional degradable and antidegradable channel: at any rate above capacity, the fidelity of every coding scheme decays exponentially with the number of channel uses. As an immediate consequence, we establish the first all-code exponential strong converse for the quantum erasure channel throughout its full parameter range, strengthening previous results that applied only to almost all codes. We also show that exponential strong-converse bounds are preserved under receiver post-processing. This yields efficiently computable semidefinite-programming bounds for arbitrary finite-dimensional channels, improved bounds for Pauli channels, and an exact exponential strong converse for a nondegradable multilevel amplitude-damping family.
