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Additivity and multiplicativity properties of some Gaussian channels for Gaussian inputs

Tohya Hiroshima
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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.

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Tohya Hiroshima. 2006-02-13. Additivity and multiplicativity properties of some Gaussian channels for Gaussian inputs. https://doi.org/10.1103/physreva.73.012330

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