Questions tagged [relative-entropy]
For questions about the (quantum) relative entropy, the quantum version of the classical Kullback-Leibler divergence.
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Does the quantum relative entropy have a direct operational interpretation?
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)\...
glS♦
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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 ...
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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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Which quantum entropies are meaningful with respect to continuous distributions of states?
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 ...
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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^{...
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