Approximate majorization and high-order capacity of quantum depolarizing channels
Abstract
A central challenge in quantum information theory is to determine whether entanglement provides an advantage for information processing when coherent operations across multiple channel uses are allowed. For depolarizing channels, King's proof of the additivity of the minimum output entropy rules out such an advantage for classical communication at leading asymptotic order, while leaving open the possibility of an advantage for higher orders. In this work, we conjecture a majorization relation for the outputs of depolarizing channels and prove an approximate version of this conjecture. Our proof combines an exact ordering of shifted log-determinants with an anti-concentration bound for the spectrum of the product-state output, refining King's analysis based on Schatten norms. As a direct application, we obtain a tight third-order expansion for the classical capacity of quantum depolarizing channels. Consequently, entangled codewords and collective decoding can improve the message size over the product-coding strategy by at most O(log log n) bits, sharpening our understanding of the role of entanglement in the finite-blocklength regime.
Related
- Optimal Approximate Quantum Conversion from a Taut-String Principle in Majorization-Based Resource Theories
- Robustness-based bounds for approximate joint realizations of incompatible quantum channels
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- Information-Spectrum General Formulas for the Capacity Region of Classical-Quantum Multiple Access Channels
- Private Capacity of Quantum Channels Induced by Non-stabilizer Environmental States
BibTeX
@misc{song2026approximate,
title = {{Approximate majorization and high-order capacity of quantum depolarizing channels}},
author = {Zhiwei Song and Xin Wang and Marco Tomamichel and Kun Fang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37240},
eprint = {2609.37240},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37240},
}
RIS
TY - UNPB
TI - Approximate majorization and high-order capacity of quantum depolarizing channels
AU - Zhiwei Song
AU - Xin Wang
AU - Marco Tomamichel
AU - Kun Fang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37240
UR - https://arxiv.org/abs/2609.37240
AB - A central challenge in quantum information theory is to determine whether entanglement provides an advantage for information processing when coherent operations across multiple channel uses are allowed. For depolarizing channels, King's proof of the additivity of the minimum output entropy rules out such an advantage for classical communication at leading asymptotic order, while leaving open the possibility of an advantage for higher orders. In this work, we conjecture a majorization relation for the outputs of depolarizing channels and prove an approximate version of this conjecture. Our proof combines an exact ordering of shifted log-determinants with an anti-concentration bound for the spectrum of the product-state output, refining King's analysis based on Schatten norms. As a direct application, we obtain a tight third-order expansion for the classical capacity of quantum depolarizing channels. Consequently, entangled codewords and collective decoding can improve the message size over the product-coding strategy by at most O(log log n) bits, sharpening our understanding of the role of entanglement in the finite-blocklength regime.
ER -