A depolarizing choir sings in Gaussian harmony
Abstract
We study the noise threshold for positive quantum capacity for the qubit depolarizing channel. We explore analytically the action of the qubit depolarizing channel on the symmetric subspaces of the input qubits, in the limit of asymptotically many uses of the channel. We observe the emergence of a bosonic Gaussian channel. Furthermore, the codes previously developed for the depolarizing channel can be translated to codes for the emergent Gaussian channel, and it is easier to further optimize these codes for the simpler emergent Gaussian channel. Translating these codes back to the depolarizing channel leads to extremely good input states for the coherent information of the depolarizing channel producing new lower bounds on the noise threshold for positive capacity. In addition to improved lower bounds on the threshold, this newly found link between depolarizing noise and Gaussian channels offers a novel perspective contributing to our understanding of these symmetric codes.
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BibTeX
@misc{ahmed2026depolarizing,
title = {{A depolarizing choir sings in Gaussian harmony}},
author = {Rabsan Galib Ahmed and Sujeet Bhalerao and Sungjai Lee and Felix Leditzky and Debbie Leung and Luke Schaeffer and Graeme Smith},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39747},
eprint = {2609.39747},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39747},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A depolarizing choir sings in Gaussian harmony
AU - Rabsan Galib Ahmed
AU - Sujeet Bhalerao
AU - Sungjai Lee
AU - Felix Leditzky
AU - Debbie Leung
AU - Luke Schaeffer
AU - Graeme Smith
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.39747
UR - https://arxiv.org/abs/2609.39747
AB - We study the noise threshold for positive quantum capacity for the qubit depolarizing channel. We explore analytically the action of the qubit depolarizing channel on the symmetric subspaces of the input qubits, in the limit of asymptotically many uses of the channel. We observe the emergence of a bosonic Gaussian channel. Furthermore, the codes previously developed for the depolarizing channel can be translated to codes for the emergent Gaussian channel, and it is easier to further optimize these codes for the simpler emergent Gaussian channel. Translating these codes back to the depolarizing channel leads to extremely good input states for the coherent information of the depolarizing channel producing new lower bounds on the noise threshold for positive capacity. In addition to improved lower bounds on the threshold, this newly found link between depolarizing noise and Gaussian channels offers a novel perspective contributing to our understanding of these symmetric codes.
ER -