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Geometric inequalities for bosonic quantum systems

February 13, 2017 - 2:00pm
Robert Koenig
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. This statement and some of its consequences are information-theoretic counterparts of certain geometric inequalities. In this talk, I will give an overview of analogous statements 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. The inequalities have application to certain semigroups as well as capacity problems.

The talk is based on joint work with Stefan Huber, Graeme Smith, and Anna Vershynina. 

CSS 3100A

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