平均态熵层次结构与通过量子卷积的经典通信
Mean-State Entropy Hierarchies and Classical Communication through Quantum Convolutions
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中文总结 AI 辅助
研究通过量子卷积建立平均态熵层次结构，利用兼容稳定器去相位等方法，给出可计算霍列沃下界，改进之前平均态界，为非稳定器三量子比特族给出单字母公式，还展示了经典和量子通信速率同时为正的共存区域。
中文摘要 AI 辅助
量子卷积提供了经典卷积的离散变量类似物，平均态捕获了在重复卷积下保持的稳定器结构。我们建立了由兼容的稳定器去相位产生的有限步熵层次结构。沿着每个兼容的各向同性标志，熵朝着平均态熵上限增加，而到平均态的相对熵距离恰好分解为连续的相干损失和最终的经典非均匀性。在兼容子空间上进行优化可得到状态的固有熵分布。对于量子卷积信道，外尔协方差将单次经典通信问题简化为最小输出熵。一个谱转移论证表明，合适的稳定器输入可将环境的稳定器测量分布再现为信道输出谱。这给出了所有完全稳定器测量的可计算霍列沃下界；其兼容限制由熵层次结构表征，并改进了Bu、Gu和Jaffe之前的平均态界。该界对于稳定器对角环境是精确的，对于其霍列沃容量是强可加的，并为一个非稳定器三量子比特族给出了单字母公式。同一族还展示了一个经典和量子通信速率同时为正的共存区域。
英文摘要
Quantum convolution provides a discrete-variable analogue of classical convolution, with the mean state capturing the stabilizer structure preserved under repeated convolution. We establish a finite-step entropy hierarchy generated by compatible stabilizer dephasings. Along every compatible isotropic flag, the entropy increases toward the mean-state entropy ceiling, while the relative-entropy distance to the mean state decomposes exactly into successive coherence losses and a terminal classical nonuniformity. Optimizing over compatible subspaces yields an intrinsic entropy profile of the state. For quantum convolutional channels, Weyl covariance reduces the one-shot classical communication problem to minimal output entropy. A spectral-transfer argument shows that suitable stabilizer inputs reproduce stabilizer-measurement distributions of the environment as channel-output spectra. This gives a computable Holevo lower bound over all complete stabilizer measurements; its compatible restriction is characterized by the entropy hierarchy and refines the previous mean-state bound of Bu, Gu, and Jaffe. The bound is exact for stabilizer-diagonal environments, for which the Holevo capacity is strongly additive, and yields a single-letter formula for a nonstabilizer qutrit family. The same family also exhibits a coexistence region with simultaneously positive classical and quantum communication rates
