Coupling Structure Determines Communication Regimes in Discrete Quantum Convolutional Channels
Abstract
We study the recently developed theory of quantum convolution for discrete-variable quantum systems. We classify the discrete quantum convolutional channels generated by an invertible 2×2 coupling matrix and a fixed environmental state according to which entries of the coupling ma- trix vanish. Under role-preserving basis relabelings, matrices with all four entries nonzero form d−2 canonical cross-ratio classes, whereas matrices with exactly one vanishing entry split into four inequivalent branches. We determine the optimized one-shot Holevo information and the classical, quantum, and private capacities for all four one-entry-vanishing branches. If a diago- nal entry vanishes, the channel is an entanglement-breaking measure-and-prepare orbit channel: its classical capacity equals a relative entropy coherence of the environmental state, whereas its quantum and private capacities vanish. If an off-diagonal entry vanishes, the channel is a degradable generalized-dephasing channel: one complete orthonormal basis is transmitted without error, whereas the quantum and private capacities are determined by the entropy deficit of the environ-ental state after dephasing in the conjugate basis. Thus, the position of a single vanishing entry selects two qualitatively different communication regimes. When all four entries are nonzero, the channels are irreducibly Weyl covariant, reducing the classical-capacity problem to a regularized minimum-output-entropy problem. For the unique fully nonzero coupling class in the single-qutrit case, we further derive an exact Holevo formula for a depolarized one-parameter family and identify its entanglement-breaking threshold.
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BibTeX
@misc{xiong2026coupling,
title = {{Coupling Structure Determines Communication Regimes in Discrete Quantum Convolutional Channels}},
author = {Chunhe Xiong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16200},
eprint = {2609.16200},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16200},
}
RIS
TY - UNPB
TI - Coupling Structure Determines Communication Regimes in Discrete Quantum Convolutional Channels
AU - Chunhe Xiong
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.16200
UR - https://arxiv.org/abs/2609.16200
AB - We study the recently developed theory of quantum convolution for discrete-variable quantum systems. We classify the discrete quantum convolutional channels generated by an invertible 2×2 coupling matrix and a fixed environmental state according to which entries of the coupling ma- trix vanish. Under role-preserving basis relabelings, matrices with all four entries nonzero form d−2 canonical cross-ratio classes, whereas matrices with exactly one vanishing entry split into four inequivalent branches. We determine the optimized one-shot Holevo information and the classical, quantum, and private capacities for all four one-entry-vanishing branches. If a diago- nal entry vanishes, the channel is an entanglement-breaking measure-and-prepare orbit channel: its classical capacity equals a relative entropy coherence of the environmental state, whereas its quantum and private capacities vanish. If an off-diagonal entry vanishes, the channel is a degradable generalized-dephasing channel: one complete orthonormal basis is transmitted without error, whereas the quantum and private capacities are determined by the entropy deficit of the environ-ental state after dephasing in the conjugate basis. Thus, the position of a single vanishing entry selects two qualitatively different communication regimes. When all four entries are nonzero, the channels are irreducibly Weyl covariant, reducing the classical-capacity problem to a regularized minimum-output-entropy problem. For the unique fully nonzero coupling class in the single-qutrit case, we further derive an exact Holevo formula for a depolarized one-parameter family and identify its entanglement-breaking threshold.
ER -