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arXiv:2607.16653

Mean-State Entropy Hierarchies and Classical Communication through Quantum Convolutions

Chunhe Xiong, Sunho Kim, Qing-hua Zhang, Shao-ming Fei, Junde Wu

quant-phSubmitted Jul 18, 2026• Announced Jul 21, 2026• 0 citations• Revised Jul 21, 2026 (v2)
v1 · Jul 18, 2026v2 · Jul 21, 2026
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Abstract

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

Comments
10pages, 2 figures, typos corrected

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