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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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Consider the quantum relative entropy, defined as $$D(\rho\|\sigma) = \operatorname{tr}(\rho\log\rho)-\operatorname{tr}(\rho\log\sigma),$$ for all $\rho,\sigma\ge0$ such that $\operatorname{im}(\rho)\... 1 vote 0 answers 31 views ### How to calculate relative entropy of coherence? Relative entropy of coherence for a density matrix p is defined as follow$C(p)=S(p_{diag})-S(p)$Where S is the von neumann entropy. for more info check the link (look at the section result) I know ... 1 vote 0 answers 32 views ### How can$\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$\...
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When using a quantum channel to transmit classical information, we consider an ensemble $\mathcal{E} = \{(\rho_x, p(x))\}$ consisting of states $\rho_x$ labelled with a symbol $x$ from a finite ...
### 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^{...