Additivity and multiplicativity properties of some Gaussian channels for Gaussian inputs

Abstract

We prove multiplicativity of maximal output $p$ norm of classical noise channels and thermal noise channels of arbitrary modes for all $p>1$ under the assumption that the input signal states are Gaussian states. As a direct consequence, we also show the additivity of the minimal output entropy and that of the energy-constrained Holevo capacity for those Gaussian channels under Gaussian inputs. To the best of our knowledge, newly discovered majorization relation on symplectic eigenvalues, which is also of independent interest, plays a central role in the proof.

9 pages, no figures. Published Version

References in corpus (7)

• Minimum output entropy of bosonic channels: a conjecture
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
• Additivity properties of a Gaussian Channel
• Minimum Renyi and Wehrl entropies at the output of bosonic channels
• Strong superadditivity of the entanglement of formation follows from its additivity
• Key distillation from Gaussian states by Gaussian operations
• Gaussian Operations and Privacy

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