Questions tagged [renyi-entropies]
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3
questions
2
votes
1answer
98 views
Prove the additivity of the Renyi entropy: $H_{\beta}(p \times r) = H_{\beta}(p) + H_{\beta}(r)$
The Renyi entropy of order $\beta$, for a discrete probability distribution $p$ is given by
\begin{equation}
H_{\beta}(p) = \frac{1}{1 - \beta} ~\log \left( \sum_{i \in S} p(i)^{\beta} \right),
\end{...
3
votes
1answer
43 views
Continuity of Renyi entropies - limiting cases
The Renyi entropies are defined as
$$S_{\alpha}(\rho)=\frac{1}{1-\alpha} \log \operatorname{Tr}\left(\rho^{\alpha}\right), \alpha \in(0,1) \cup(1, \infty)$$
It is claimed that this quantity is ...
1
vote
1answer
27 views
How to take the limits of the sandwiched Renyi divergences?
The sandwiched Renyi divergence is defined as
$$\begin{equation}
\tilde{D}_{\alpha}(\rho \| \sigma):=\frac{1}{\alpha-1} \log \operatorname{tr}\left[\left(\sigma^{\frac{1-\alpha}{2 \alpha}} \rho \...