Energy-constrained two-way capacities of the pure-loss channel

We determine the two-way quantum and secret-key capacities of the pure-loss channel under an average input photon-number constraint. For transmissivity $η$ and photon budget $N$, both capacities equal $g(N)-g((1-η)N)$, where $g$ is the entropy of a thermal state. This coincides with the rate achieved by the known reverse coherent information of a two-mode squeezed vacuum. Our result provides the last missing capacity formula for the celebrated pure-loss channel, completing the picture of bosonic quantum communication under pure loss.

Source: arXiv:2610.12365v1 - http://arxiv.org/abs/2610.12365v1 PDF: https://arxiv.org/pdf/2610.12365v1 Original Link: http://arxiv.org/abs/2610.12365v1