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# Questions tagged [relative-entropy]

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

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### What is the Bregman projection of $\rho+\epsilon X$ onto the space of states?

Notation: Let $S(X)=\operatorname{tr}[X\log X]$ for any $X\geq0$ be the von Neumann entropy and let $D_S(X,Y)=\operatorname{tr}[X\log X-X\log Y -X+Y]$ be the corresponding Bregman divergence (which is ...
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### 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 ...
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### Quantum Relative entropy- the math and intuition

I am new to quantum information theory and have been reading Mark Wilde's notes on quantum relative entropy. http://www.markwilde.com/teaching/2015-fall-qit/lectures/lecture-19.pdf I have three basic ...
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### How to calculate the conditional min-entropy via a semidefinite program?

I am trying to formulate the calculation of conditional min-entropy as a semidefinite program. However, so far I have not been able to do so. Different sources formulate it differently. For example, ...
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