Energy-constrained two-way capacities of pure-loss and quantum-limited amplifier channels
Abstract
We determine the two-way quantum, entanglement-distribution, private, and secret-key capacities of the pure-loss bosonic channel under an unconditional mean transmitted-photon-number constraint. For transmissivity η and mean photon number N, all four capacities coincide and are given by $g(N)-g((1-η)N)$, where g is the entropy of a thermal mode. This resolves the longstanding energy-constrained capacity problem by establishing the optimality of the reverse-coherent-information rate introduced in 2009. Our central tool is sector teleportation simulation, which we develop specifically to transfer the input-energy constraint to the shared entanglement resource, thereby preserving the constraint throughout converse arguments for general adaptive protocols. For every N>0, we further show that the corresponding strong-converse thresholds coincide with the unconstrained value −log2(1−η). For parallel protocols with a hard total-photon-number cutoff, the same energy-constrained capacity formula instead satisfies an exponential strong converse. As an extension, we determine the energy-constrained two-way capacities of the quantum-limited amplifier, showing that classical assistance does not improve its unassisted quantum and private rates. Together, these results establish a unified finite-energy framework for adaptive bosonic communication and reveal how energy constraints fundamentally reshape both attainable rates and converse bounds.
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BibTeX
@misc{pirandola2026energyconstrained,
title = {{Energy-constrained two-way capacities of pure-loss and quantum-limited amplifier channels}},
author = {Stefano Pirandola},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06832},
eprint = {2610.06832},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06832},
}
RIS
TY - UNPB
TI - Energy-constrained two-way capacities of pure-loss and quantum-limited amplifier channels
AU - Stefano Pirandola
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.06832
UR - https://arxiv.org/abs/2610.06832
AB - We determine the two-way quantum, entanglement-distribution, private, and secret-key capacities of the pure-loss bosonic channel under an unconditional mean transmitted-photon-number constraint. For transmissivity η and mean photon number N, all four capacities coincide and are given by $g(N)-g((1-η)N)$, where g is the entropy of a thermal mode. This resolves the longstanding energy-constrained capacity problem by establishing the optimality of the reverse-coherent-information rate introduced in 2009. Our central tool is sector teleportation simulation, which we develop specifically to transfer the input-energy constraint to the shared entanglement resource, thereby preserving the constraint throughout converse arguments for general adaptive protocols. For every N>0, we further show that the corresponding strong-converse thresholds coincide with the unconstrained value −log_2(1−η). For parallel protocols with a hard total-photon-number cutoff, the same energy-constrained capacity formula instead satisfies an exponential strong converse. As an extension, we determine the energy-constrained two-way capacities of the quantum-limited amplifier, showing that classical assistance does not improve its unassisted quantum and private rates. Together, these results establish a unified finite-energy framework for adaptive bosonic communication and reveal how energy constraints fundamentally reshape both attainable rates and converse bounds.
ER -