Exact strong-converse thresholds for noisy Gaussian channels

Determine the exact strong-converse thresholds for the energy-constrained capacities of thermal-loss, noisy-amplifier, and additive-Gaussian-noise bosonic channels.

Background

The paper establishes energy-constrained weak-converse upper bounds for two-way quantum, entanglement-distribution, private, and secret-key capacities of thermal-loss, noisy-amplifier, and additive-noise Gaussian channels. These bounds apply in the vanishing-error asymptotic regime and do not by themselves imply a strong converse, in part because public vacuum dilution under an unconditional mean-energy constraint prevents a direct inference of energy-dependent strong-converse behavior from the weak-converse result.

The unresolved problem is to identify the precise strong-converse thresholds for the noisy channel families considered. Such thresholds would characterize the maximum asymptotic rates achievable when the error is required to converge to one above the relevant capacity threshold, thereby extending the paper's weak-converse analysis to strong-converse behavior.