Bosonic quantum communication beyond the thermal threshold

Abstract

The quantum capacity of the bosonic thermal attenuator, which is given by the regularization of its coherent information, is unknown. The seminal work of Holevo and Werner established in 1999 the standard one-use lower bound obtained from input thermal states. We first prove that this long-standing lower bound is the exact supremum over all single-mode Gaussian states and then show that, crucially, a non-Gaussian state can do better. As a consequence, we prove positivity of the quantum capacity in a parameter region where the channel is not antidegradable, yet its coherent information optimized over single-mode Gaussian states vanishes. For example, with one thermal photon in the environment and at transmissivity $η=0.8$, the coherent information is non-positive for every single-mode Gaussian input. We give an explicit rank-two non-Gaussian state, supported on only six Fock levels, whose coherent information is certified to be at least $4.7\times10^{-4}$ qubits per channel use. This short witness is far from numerically optimal: a numerical optimization over fixed non-Gaussian families reaches at least $8.4\times 10^{-3}$ qubits per channel use at the same point. More generally, at $ν=1$, using non-Gaussian inputs we certify positivity of the coherent information, and therefore of the quantum capacity, down to $η=0.7841$; by contrast, the channel is antidegradable, and hence has zero quantum capacity, for $η\leq0.75$. Overall, our work identifies new high-noise regimes in which bosonic quantum communication is possible.