Norms of quantum Gaussian multi-mode channels

Abstract

We compute the ${\mathcal{S}}^p\to {\mathcal{S}}^p$ norm of a general Gaussian gauge-covariant multi-mode channel for any $1\le p<\infty$, where ${\mathcal{S}}^p$ is a Schatten space. As a consequence, we verify the Gaussian optimizer conjecture and the multiplicativity conjecture in these cases.

9 pages; minor changes; to appear in J. Math. Phys

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