Classical Capacity and Entanglement Cost of the Amplitude Damping Channel
Abstract
Determining a noisy quantum channel's classical capacity and entanglement cost generally requires regularization over many channel uses. We remove both regularizations for every qubit-to-qubit channel admitting a pure output. For each such channel, Holevo information, channel entanglement of formation, and parallel entanglement cost are additive with those of any finite-dimensional partner channel. This class includes all qubit-to-qubit channels of Kraus rank at most two. For the amplitude damping channel with damping probability p, the unassisted classical capacity equals the known single-use Holevo information, attained by a binary pure-state ensemble with collective decoding, and the entanglement cost is h2((1+√p)/2) ebits per use. The common mechanism is a support criterion for strong superadditivity of entanglement of formation: one marginal has no support on the sector in which both local systems are orthogonal to fixed distinguished vectors. We prove this criterion in arbitrary finite dimensions using a triangular block-matrix entropy inequality and decompositions preserving two expectations. For amplitude damping, we also derive an exact finite-block Holevo deficit, identify the unique optimal average input for p<1, and construct a binary Kraus representation attaining the uniform formation bound.
Related
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BibTeX
@misc{tang2026classical,
title = {{Classical Capacity and Entanglement Cost of the Amplitude Damping Channel}},
author = {Ziao Tang and Chengkai Zhu and Ge Bai and Xin Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28592},
eprint = {2609.28592},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28592},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classical Capacity and Entanglement Cost of the Amplitude Damping Channel
AU - Ziao Tang
AU - Chengkai Zhu
AU - Ge Bai
AU - Xin Wang
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28592
UR - https://arxiv.org/abs/2609.28592
AB - Determining a noisy quantum channel's classical capacity and entanglement cost generally requires regularization over many channel uses. We remove both regularizations for every qubit-to-qubit channel admitting a pure output. For each such channel, Holevo information, channel entanglement of formation, and parallel entanglement cost are additive with those of any finite-dimensional partner channel. This class includes all qubit-to-qubit channels of Kraus rank at most two. For the amplitude damping channel with damping probability p, the unassisted classical capacity equals the known single-use Holevo information, attained by a binary pure-state ensemble with collective decoding, and the entanglement cost is h_2((1+√p)/2) ebits per use. The common mechanism is a support criterion for strong superadditivity of entanglement of formation: one marginal has no support on the sector in which both local systems are orthogonal to fixed distinguished vectors. We prove this criterion in arbitrary finite dimensions using a triangular block-matrix entropy inequality and decompositions preserving two expectations. For amplitude damping, we also derive an exact finite-block Holevo deficit, identify the unique optimal average input for p<1, and construct a binary Kraus representation attaining the uniform formation bound.
ER -