A Solution of Gaussian Optimizer Conjecture for Quantum Channels

V. Giovannetti, A. S. Holevo, R. García-Patrón

Research output: Contribution to journalArticlepeer-review


The long-standing conjectures of the optimality of Gaussian inputs and additivity are solved for a broad class of gauge-covariant or contravariant bosonic Gaussian channels (which includes in particular thermal, additive classical noise, and amplifier channels) restricting to the class of states with finite 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.
Original languageEnglish
Pages (from-to)1553-1571
Number of pages19
JournalCommunications in Mathematical Physics
Issue number3
Early online date27 Aug 2014
Publication statusPublished - 31 Mar 2015


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