The Rényi entropy of order $\alpha$ of a PSD matrix $\rho$ is defined as

$$H_{\alpha}(\rho)=\frac{1}{1-\alpha}\log_2\left(\frac{\mathrm{Tr}\left[\rho^{\alpha}\right]}{\mathrm{Tr}[\rho]}\right)$$

for all $\alpha\in(0, 1)\cup(1,+\infty)$. It can be extended in $\alpha=0$, resulting in the Hartley entropy $\log_2\left(\mathrm{rank}(\rho)\right)$, in $\alpha=1$, resulting in the Von Neumann entropy, and in $\alpha=+\infty$, resulting in the min-entropy, as seen in 1306.3142.

These entropies are more and more studied in finite-size quantum cryptography. As such, it could be interesting to include them in toqito.