# Questions tagged [min-entropy]

The smallest of the Rényi family of entropies, corresponding to the most conservative way of measuring the unpredictability of a set of outcomes, as the negative logarithm of the probability of the most likely outcome.

3 questions
Filter by
Sorted by
Tagged with
135 views

### How to prove that $\frac{| x_0 \rangle + | x_1 \rangle}{\sqrt{2}}$ hides one of $x_0$ or $x_1$?

I create a quantum state $| \psi \rangle = \frac{| x_0 \rangle + | x_1 \rangle}{\sqrt{2}}$ for a randomly chosen $x_0,x_1$ of 50 bits. I give this quantum state $|\psi \rangle$ to you and you return ...
### Prove that for a cq-state $\rho_{XE}$, $H_\infty(X|E) \ge H_\infty(X) - \log|E|$
Given a classical-quantum(cq) state $\rho_{XE}$, where the $X$ register is classical, I want to prove the following: \begin{align} H_\infty(X|E) \ge H_\infty(X) - \log|E|,\tag{1} \end{align} i.e....
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 ...