# Questions tagged [max-entropy]

For questions about the max entropy (also called Hartley entropy) or max-relative entropy functions.

11 questions
Filter by
Sorted by
Tagged with
20 views

### Max-relative entropy quasi-convexity inequality under partial trace

The max-relative entropy between two states is defined as $$D_{\max }(\rho \| \sigma):=\log \min \{\lambda: \rho \leq \lambda \sigma\}.$$ It is known that the max-relative entropy is quasi-convex. ...
34 views

### Quasi concavity of max-relative entropy?

The max-relative entropy between two states is defined as $$D_{\max }(\rho \| \sigma):=\log \min \{\lambda: \rho \leq \lambda \sigma\}.$$ It is known that the max-relative entropy is quasi-convex. ...
62 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 ...
114 views

### Continuity bounds on $D_{\max}(\rho_{AB}\|\rho_A\otimes\rho_B)$

The max-relative entropy between two states is defined as $$D_{\max }(\rho \| \sigma):=\log \min \{\lambda: \rho \leq \lambda \sigma\},$$ where $\rho\leq \sigma$ should be read as $\sigma - \rho$ is ...
58 views

### When can the max relative entropy be written as $D_{\max}(\rho\|\sigma) = \|\sigma^{-1/2}\rho\sigma^{-1/2}\|_{\infty}$?

The max-relative entropy between two states is defined as $D_{\max}(\rho\|\sigma) = \log\lambda$, where $\lambda$ is the smallest real number that satisfies $\rho\leq \lambda\sigma$, where $A\leq B$ ...
100 views

### Questions about the relation between max-relative entropy $D_{\max}(\rho||\sigma)$ and max-information

The max-relative entropy between two states is defined as $$D_{\max }(\rho \| \sigma):=\log \min \{\lambda: \rho \leq \lambda \sigma\},$$ where $\rho\leq \sigma$ should be read as $\sigma - \rho$ is ...
52 views

### Do we know the limits of the quantum Tsallis entropy?

From the two main generalizations of the von Neumann entropy: $$S(\rho)=-\operatorname{Tr}(\rho \log \rho)$$ meaning Rényi: R_{\alpha}(\rho)=\frac{1}{1-\...
103 views

### Relating quantum max-relative entropy to classical maximum entropy

The quantum max-relative entropy between two states is defined as $$D_{\max }(\rho \| \sigma):=\log \min \{\lambda: \rho \leq \lambda \sigma\},$$ where $\rho\leq \sigma$ should be read as \$\sigma - \...
41 views

### What is the relationship between these two definitions for the max-entropy?

On Wikipedia, the max-entropy for classical systems is defined as $$H_{0}(A)_{\rho}=\log \operatorname{rank}\left(\rho_{A}\right)$$ The term max-entropy in quantum information is reserved for the ...