TITLE: Subadditivity for Renyi entropies
QUESTION [10 upvotes]: Do the Renyi entropies satisfy the standard subadditivity of Shannon entropy? That is, 
\begin{equation}
H_\alpha(A,B) \leq H_\alpha(A) + H_\alpha(B)  ? 
\end{equation}
for $\alpha \ne 1$. If they do, for which $\alpha$? 
Here $H_\alpha(X)$ is the standard Renyi $\alpha$-entropy of the random variable X,
\begin{equation}
H_\alpha(X)=\frac{1}{1-\alpha}\log\sum_i^n p_i^\alpha,
\end{equation}
and $H_\alpha(A,B)$ is the Renyi entropy of the joint probability distribuition of the random variables A and B.

REPLY [2 votes]: In fact, to find a violation of any linear inequality you could form using the Renyi entropies of order $\alpha \in (0,1) \cup (1,\infty)$, please consult the following paper:
http://arxiv.org/abs/1212.0248