Entropy power inequalities for bosonic quantum systems

Interactions between Partial Differential Equations & Functional Inequalities

08 December 17:00 - 17:25

Robert König - TU Munich

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. My talk is based on joint work with Stefan Huber, Graeme Smith, and Anna Vershynina.
José A. Carrillo
Imperial College London
Ivan Gentil
Institut Camille Jordan
Helge Holden
NTNU - Norwegian University of Science and Technology
Cédric Villani
Institut Henri Poincaré (IHP)
Boguslaw Zegarlinski
Imperial College London


José A. Carrillo


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