Strong subadditivity of the Renyi entropies for bosonic and fermionic Gaussian states

Recently, there has been a surge of interest in using Renyi entropies as quantifiers of correlations in many-body quantum systems. However, it is well known that in general these entropies do not satisfy the strong subadditivity inequality, which is a central property ensuring the positivity of correlation measures. In fact, in many cases they do not even satisfy the weaker condition of subadditivity. In the present paper we shed light on this subject by providing a detailed survey of Renyi entropies for bosonic and fermionic Gaussian states. We show that for bosons the Renyi entropies always satisfy subadditivity, but not necessarily strong subadditivity. Conversely, for fermions both do not hold in general. We provide the precise intervals of the Renyi index alpha for which subadditivity and strong subadditivity are valid in each case. (AU)