Robert König: Entropy power inequalities for bosonic quantum systems

Abstract: Shannon's entropy power inequality gives a lower bound on the entropy power of the sum of two independent random variables in terms of the individual entropy powers. In this talk, I will give an overview of analogous inequalities for bosonic quantum systems. The first concerns a certain convolution operation between two quantum states: here two independent bosonic modes combine at a beamsplitter. The second involves an operation (originally introduced by Werner) combining a probability distribution on phase space with a quantum state of a bosonic mode. Our proofs are similar in spirit to standard classical proofs. Specifically, we use a quantum de Bruijin identity relating entropy production under a quantum diffusion process to a divergence-based quantum Fisher information.