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Exact series formulas for the capacities of the amplitude damping channel
Abstract
We derive explicit, absolutely convergent series formulas for the quantum, unassisted classical, and entanglement-assisted classical capacities of the qubit amplitude damping channel, eliminating residual optimizations and implicit roots. We also obtain analytical upper and lower bounds on two-way assisted quantum and private communication capacities by evaluating a balanced-squashing bound and optimizing the reverse coherent information. Our results characterize the optimal input populations, establish convergence and truncation properties, and provide analytical benchmarks for quantum and classical communication over dissipative channels.
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BibTeX
@misc{pirandola2026exact,
title = {{Exact series formulas for the capacities of the amplitude damping channel}},
author = {Stefano Pirandola},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31609},
eprint = {2609.31609},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31609},
}
RIS
TY - UNPB
TI - Exact series formulas for the capacities of the amplitude damping channel
AU - Stefano Pirandola
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31609
UR - https://arxiv.org/abs/2609.31609
AB - We derive explicit, absolutely convergent series formulas for the quantum, unassisted classical, and entanglement-assisted classical capacities of the qubit amplitude damping channel, eliminating residual optimizations and implicit roots. We also obtain analytical upper and lower bounds on two-way assisted quantum and private communication capacities by evaluating a balanced-squashing bound and optimizing the reverse coherent information. Our results characterize the optimal input populations, establish convergence and truncation properties, and provide analytical benchmarks for quantum and classical communication over dissipative channels.
ER -