Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 334, Issue 3, Pages 1553-1571Publisher
SPRINGER
DOI: 10.1007/s00220-014-2150-6
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Funding
- Isaac Newton Institute for Mathematical Sciences, Cambridge, UK
- Rothschild Distinguished Visiting Fellowship
- RAS Fundamental Research Programs
- Russian Quantum Center
- RFBR [12-01-00319]
- Alexander von Humboldt Foundation
- F.R.S.-FNRS [T.0199.13]
- Action Back to Belgium Grants of the Belgian Federal Science Policy
- HIPERCOM
- Inter-university Attraction Poles program of the Belgian Science Policy Office [IAP P7-35]
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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.
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