Transport and Channel Normal Forms for Clifford Interactions
Abstract
We study how Clifford interactions with a fixed environment determine quantum transmission, in a setting that extends positive discrete quantum convolution . We characterize when Clifford operations on the environment can be replaced by operations on the signal input and the two outputs, and classify the interactions under local Clifford transformations . For pure stabilizer environments, we determine the noiseless, dephasing, and completely depolarizing parts of the channel directly from the interaction and environmental stabilizers, obtaining its quantum and private capacities . This reveals a distinction between interactions: those locally equivalent to positive convolution produce entanglement-breaking channels for every pure stabilizer environment, whereas every other interaction in the class admits noiseless quantum transmission with a suitable pure stabilizer environment . For positive convolution, environmental Clifford transport also allows us to separate the stabilized coordinates of an arbitrary mixed environment . These coordinates carry only a classical label shared by the receiver and environment, so removing them preserves quantum and private capacities . The resulting channel reduction yields a private-capacity bound by the modified relative entropy of magic of the environmental state .
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BibTeX
@misc{chunhe2026transport,
title = {{Transport and Channel Normal Forms for Clifford Interactions}},
author = {Xiong Chunhe and Kim Sunho and Zhang Qing-Hua and Fei Shao-Ming and Wu Junde},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30125},
eprint = {2609.30125},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30125},
}
RIS
TY - UNPB
TI - Transport and Channel Normal Forms for Clifford Interactions
AU - Xiong Chunhe
AU - Kim Sunho
AU - Zhang Qing-Hua
AU - Fei Shao-Ming
AU - Wu Junde
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30125
UR - https://arxiv.org/abs/2609.30125
AB - We study how Clifford interactions with a fixed environment determine quantum transmission, in a setting that extends positive discrete quantum convolution . We characterize when Clifford operations on the environment can be replaced by operations on the signal input and the two outputs, and classify the interactions under local Clifford transformations . For pure stabilizer environments, we determine the noiseless, dephasing, and completely depolarizing parts of the channel directly from the interaction and environmental stabilizers, obtaining its quantum and private capacities . This reveals a distinction between interactions: those locally equivalent to positive convolution produce entanglement-breaking channels for every pure stabilizer environment, whereas every other interaction in the class admits noiseless quantum transmission with a suitable pure stabilizer environment . For positive convolution, environmental Clifford transport also allows us to separate the stabilized coordinates of an arbitrary mixed environment . These coordinates carry only a classical label shared by the receiver and environment, so removing them preserves quantum and private capacities . The resulting channel reduction yields a private-capacity bound by the modified relative entropy of magic of the environmental state .
ER -