Skip to main content

Questions tagged [relative-entropy]

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

7 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
3 votes
0 answers
42 views

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
0 answers
27 views

What are examples of states saturating the strong subadditivity of the von Neumann entropy?

A well-known property of classical distribution is that they satisfy strong subadditivity, meaning that for any tripartite joint probability distribution $p(x,y,z)$, we have the inequality $$H(AB)+H(...
glS's user avatar
  • 25.5k
2 votes
0 answers
72 views

On the use of $\log(P\otimes Q)= \log P\otimes I+I\otimes\log Q$ for relations between entropic quantities. What if $P,Q$ are only semidefinite?

Many properties of entropic quantities are shown by resorting to related properties of the relative entropy of suitable quantities. For instance, subadditivity of entropy may follow from non ...
atlantropa's user avatar
2 votes
2 answers
145 views

Exercise 11.7 in Nielsen & Chuang and basic properties of Shannon entropy

I apologize in advance if this question is trivial, I'm aware I'm a total beginner in this field. This is the exercise I would like to solve: As to the first point, what I get is that one should ...
atlantropa's user avatar
1 vote
0 answers
53 views

How to calculate relative entropy of coherence?

Relative entropy of coherence for a density matrix p is defined as follow $C(p)=S(p_{diag})-S(p)$ Where S is the von neumann entropy. for more info check the link (look at the section result) I know ...
reza's user avatar
  • 741
1 vote
0 answers
34 views

How can $\chi(\hat{A},\hat{B}:C) \le \chi(\hat{A},B:C)$ be true?

The holevo information of $\rho_{ABC}$ w.r.t to measurements on A and B (for the sake of this we'll assume local measurements suffice), is given by $$\chi(\hat{A},\hat{B}:C)$$ where $\hat{A}$ and $\...
GaussStrife's user avatar
  • 1,115
1 vote
0 answers
29 views

Find the minimal and maximal of $\widehat{S}_f (\rho \| U^* \sigma U)$

I have been study the minimal (maximal) of a $f-$divergence. Fumio Hiai introduced the $\widehat{S}_f (\rho \| \sigma)$ divergence in his article. $$\widehat{S}_f (\rho \| \sigma) := \text{Tr} \sigma^{...
Minh's user avatar
  • 111