Capacities of Quantum Amplifier Channels

Quantum amplifier channels are at the core of several physical processes in nature. Not only do they model the optical process of spontaneous parametric down-conversion, but the Bogoliubov transformation corresponding to an amplifier channel also describes the physics of the dynamical Casimir effect in superconducting circuits, the Unruh effect, and Hawking radiation. Here we study the communication capabilities of quantum amplifier channels. Provided that a particular minimum output entropy conjecture is true, we determine capacities of quantum amplifier channels in three different scenarios. First, we establish the capacities of the quantum-limited amplifier channel for one of the most general communication tasks, characterized by the trade-off between classical communication, quantum communication, and entanglement generation or consumption. Second, we establish capacities of the quantum-limited amplifier channel for the trade-off between public classical communication, private classical communication, and secret key generation. In these settings, we find that capacities decrease with increasing amplifier gain, due to unavoidable quantum-mechanical amplification noise. Third, we determine the capacity region for a singlesender, two-receiver broadcast channel induced by a unitary dilation of the quantum amplifier channel, and we also show that a fully quantum strategy outperforms those achieved by classical coherent detection strategies. Finally, we provide compelling evidence that the needed minimum output entropy conjecture is true.