Capacities of quantum amplifier channels

Abstract

Quantum amplifier channels are at the core of several physical processes. Not only do they model the optical process of spontaneous parametric down-conversion, but the 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. Invoking a recently established minimum output-entropy theorem for single-mode phase-insensitive Gaussian channels, we determine capacities of quantum-limited amplifier channels in three different scenarios. First, we establish the capacities of quantum-limited amplifier channels 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 quantum-limited amplifier channels for the trade-off between public classical communication, private classical communication, and secret key generation. Third, we determine the capacity region for a broadcast channel induced by the quantum-limited amplifier channel, and we also show that a fully quantum strategy outperforms those achieved by classical coherent detection strategies. In all three scenarios, we find that the capacities significantly outperform communication rates achieved with a naive time-sharing strategy.

Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels

“…This result finally permits to extend the Entropy Power Inequality to the quantum regime, and to prove the optimality of Gaussian encodings for both the triple trade-off coding and broadcast communication with the quantumlimited amplifier [35]. The future challenge is the extension of our result to the multimode scenario.…”

“…Our result both extends the EPI to the quantum regime and generalizes the unconstrained minimum output entropy conjecture of [7,[27][28][29], that has permitted to determine the classical capacity of any phase-covariant quantum Gaussian channel [30] (see also [34]). Our result is necessary to prove the converse theorems that guarantee the optimality of Gaussian encodings for two communication tasks involving the quantumlimited amplifier [35]. The first is the triple trade-off coding [36], that allows to simultaneously transmit both classical and quantum information and to generate shared entanglement, or to simultaneously transmit both public and private classical information and to generate a shared secret key.…”

Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels

“…The second equality follows from the formula for the energyconstrained quantum capacity of a quantum-limited amplifier channel with gain G¢ and input mean photon number N S [QW17]. Since a quantum-limited amplifier channel is a degradable channel [CG06, WPGG07], its energy-constrained private capacity is the same as its energy-constrained quantum capacity.…”

“…For the particular case of bosonic Gaussian channels, formulas for the energy-constrained quantum and private capacities of the single-mode pure-loss channel were conjectured in [GSE08] and proven in [WHG12,WQ16]. Also, for a single-mode quantum-limited amplifier channel, the energy-constrained quantum and private capacities have been established in [WQ16,QW17].…”

New Lower Bounds to the Output Entropy of Multi-Mode Quantum Gaussian Channels

“…Similarly to the quantum degraded Gaussian broadcast channel, even if Conjecture 1 still lacks a proof we can still determine bounds to the triple trade-off regions of the quantum-limited attenuator. The first of these bounds follows from the quantum Entropy Power Inequality [41,Appendix C]. The following Theorem 11 shows that any lower bound to the output entropy of the multi-mode quantum-limited attenuators in terms of the input entropy implies a bound to their triple trade-off regions.…”