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A solution of the Gaussian optimizer conjecture

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Mathematical Challenges in Quantum Information

The long-standing conjectures of the optimality of Gaussian inputs for Gaussian channel and Gaussian additivity are solved for a broad class of covariant or contravariant Bosonic Gaussian channels (which includes in particular thermal, additive classical noise, and ampli?er channels) restricting to the class of states with ?nite second moments. We show that the vacuum is the input state which minimizes the entropy at the output of such channels. This allows us to show also that the classical capacity of these channels (under the input energy constraint) is additive and is achieved by Gaussian encodings.

This talk is part of the Isaac Newton Institute Seminar Series series.

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