Gaussian optimizers and other topics in quantum information

Understand

The main topic of this thesis is the proof of two fundamental entropic inequalities for quantum Gaussian channels.

• Quantum Gaussian channels model the propagation of electromagnetic waves through optical fibers and free space in the quantum regime, and provide the mathematical model to determine the maximum rates achievable by quantum communication devices for communication and quantum key distribution.
• The first inequality proven in this thesis is the quantum Entropy Power Inequality, which provides a lower bound to the output entropy of the beam-splitter or of the squeezing in terms of the entropies of the two inputs.
• The second inequality states that Gaussian states minimize the output entropy of the one-mode quantum Gaussian attenuator among all the input states with a given entropy, and was a longstanding conjecture in quantum communication theory.