2
Suppose I have a parameterized quantum state: $\rho(\theta) = U(\theta) \rho U^\dagger(\theta)$. I am curious to know whether the following holds:
$\frac{\partial \text{Tr}_A (\rho(\theta))}{\partial \theta} = \text{Tr}_A \Big(\frac{\partial \rho(\theta)}{\partial \theta} \Big)$, where $\text{Tr}...