Nonnegativity of quantum relative entropy
= Nonnegativity of quantum relative entropy
{title2=$D(\rho\|\sigma)\geq0$}
For <density operators>, <Klein's inequality> gives $D(\rho\|\sigma)\geq0$, with equality exactly when $\rho=\sigma$. If the <support of a positive operator> $\rho$ is not contained in that of $\sigma$, the <quantum relative entropy> is $+\infty$.