 Additivity of quantum relative entropy

ID: additivity-of-quantum-relative-entropy

D (ρ_{A} \otimes ρ_{B} ∥ σ_{A} \otimes σ_{B}) = D (ρ_{A} ∥ σ_{A}) + D (ρ_{B} ∥ σ_{B}) .

This follows by expanding

lo g (σ_{A} \otimes σ_{B}) = lo g σ_{A} \otimes I + I \otimes lo g σ_{B}

and its counterpart for

ρ

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