A general attenuator ${\mathrm{\Phi }}_{\lambda ,\sigma }$ is a bosonic quantum channel that acts by combining the input with a fixed environment state $\sigma$ in a beam splitter of transmissivity $\lambda$. If $\sigma$ is a thermal state, the resulting channel is a thermal attenuator, whose quantum capacity vanishes for $\lambda \le 1/2$. We study the quantum capacity of these objects for generic $\sigma$, proving a number of unexpected results. Most notably, we show that for any arbitrary value of $\lambda >0$ there exists a suitable single-mode state $\sigma (\lambda )$ such that the quantum capacity of ${\mathrm{\Phi }}_{\lambda ,\sigma (\lambda )}$ is larger than a universal constant $c>0$. Our result holds even when we fix an energy constraint at the input of the channel, and implies that quantum communication at a constant rate is possible even in the limit of arbitrarily low transmissivity, provided that the environment state is appropriately controlled. We also find examples of states $\sigma$ such that the quantum capacity of ${\mathrm{\Phi }}_{\lambda ,\sigma }$ is not monotonic in $\lambda$. These findings may have implications for the study of communication lines running across integrated optical circuits, of which general attenuators provide natural models.

• Received 31 March 2020
• Accepted 29 July 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.110504