Upper bounds on the quantum capacity for general attenuator and amplifier

Abstract

There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises, including squeezing or even non-Gaussian one. We derive new upper bounds on the energy-constrained quantum capacity of those channels by using the quantum conditional entropy power inequality. Also, we obtain lower bounds for the same channels by means of Gaussian optimizer with fixed input entropy. They give narrow bounds when the transmissivity is near unity and the energy of input state is low.

arXiv comment6 pages, 5 figures; 1 figure added and references are updated

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• Estimating Quantum and Private capacities of Gaussian channels via degradable extensions
• Bosonic quantum communication across arbitrarily high loss channels
• Refined diamond norm bounds on the emergence of objectivity of observables
• Upper bounds on the private capacity for bosonic Gaussian channels
• Quantum Rényi Entropy Functionals for Bosonic Gaussian Systems
• Classical capacity of quantum non-Gaussian attenuator and amplifier channels
• Weighted $p$-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory