We correct an intermediate step in the derivation of our main statements in  [1] . Specifically, inequality (63) in the mentioned paper, intended to give an upper bound on the entropy of certain Gaussian states, is incorrect. In that paper, we used inequality (63) to derive the asymptotic (large-time) scaling of the entropy under the quantum version of the heat equation. We provide alternative derivations of this result, which sidestep the bound (63). The main conclusions of the paper therefore remain unaffected. We thank Giacomo de Palma, Andrea Mari and Vittorio Giovannetti for pointing out this issue, and simultaneously providing us with a resolution in a very detailed communication. We also thank them for their permission to include their discussion in this erratum. We note that one of the alternative derivations of the asymptotic scaling presented here has previously appeared in their publication.
['Robert König', 'Graeme Smith']
Corrections to “The Entropy Power Inequality for Quantum Systems”