No advantage from classical assistance for energy-constrained bosonic dephasing channels
Abstract
We prove that four capacities of single-mode bosonic dephasing channels coincide under an average photon-number constraint: the unassisted quantum capacity, the unassisted private capacity, the two-way classically assisted quantum capacity, and the two-way public-classically assisted private capacity. The assistance may be interactive: the parties can exchange classical messages between channel uses and choose subsequent inputs based on earlier outcomes. For every finite value of the constraint, their common value is the coherent information optimized over Fock-diagonal input states satisfying the constraint. The proof uses a relative entropy comparison with the completely dephasing channel to derive chain rules for the Rains relative entropy and the relative entropy of entanglement. These chain rules give an upper bound on the rates achievable by adaptive protocols whose mean input photon number is constrained on average over all channel uses. We also show that both chain rules are attained by canonical purifications of finite-energy Fock-diagonal states.
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BibTeX
@misc{arqand2026advantage,
title = {{No advantage from classical assistance for energy-constrained bosonic dephasing channels}},
author = {Amir Arqand and Graeme Smith},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13854},
eprint = {2610.13854},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13854},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - No advantage from classical assistance for energy-constrained bosonic dephasing channels
AU - Amir Arqand
AU - Graeme Smith
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13854
UR - https://arxiv.org/abs/2610.13854
AB - We prove that four capacities of single-mode bosonic dephasing channels coincide under an average photon-number constraint: the unassisted quantum capacity, the unassisted private capacity, the two-way classically assisted quantum capacity, and the two-way public-classically assisted private capacity. The assistance may be interactive: the parties can exchange classical messages between channel uses and choose subsequent inputs based on earlier outcomes. For every finite value of the constraint, their common value is the coherent information optimized over Fock-diagonal input states satisfying the constraint. The proof uses a relative entropy comparison with the completely dephasing channel to derive chain rules for the Rains relative entropy and the relative entropy of entanglement. These chain rules give an upper bound on the rates achievable by adaptive protocols whose mean input photon number is constrained on average over all channel uses. We also show that both chain rules are attained by canonical purifications of finite-energy Fock-diagonal states.
ER -