Skip to main content

Questions tagged [relative-entropy]

For questions about the (quantum) relative entropy, the quantum version of the classical Kullback-Leibler divergence.

Filter by
Sorted by
Tagged with
5 votes
1 answer

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 ...
user1936752's user avatar
  • 3,033
3 votes
0 answers

Proof that the relative entropy satisfies $S(\rho\|\sigma)=S(T\rho\|T\sigma)$ iff $\hat TT\rho=\rho$, $\hat TT\sigma=\sigma$ for some $\hat T$

To prove the saturation condition for the strong subadditivity of the von Neumann entropy, the authors of [HJPW2004] make use of the following characterisation of when the monotonicity of the ...
glS's user avatar
  • 25.5k
3 votes
2 answers

What is the conditional min-entropy for diagonal ("classical") matrices?

The conditional min-entropy, discussed e.g. in these notes by Watrous, as well as in this other post, can be defined as $$\mathsf{H}_{\rm min }(\mathsf{X} \mid \mathsf{Y})_{\rho}\equiv -\inf _{\sigma \...
glS's user avatar
  • 25.5k