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My Question: Suppose $\sigma(0)$ is trace 1, Hermitian and positive. This means that $\varrho(0)$ is also trace 1, Hermitian and positive. Are these properties preserved for $\varrho(t)$ with $t>0$? … Here are my thoughts: Preservation of Trace: taking the trace of the above evolution equation yields $\mathrm{Tr}[\dot{\varrho}_I(t)]=0$ because the equation contains commutators of finite-dimensional …

If you were to compute a trace using these states as a basis, how would you do this? …

I know that one of the requirements for a density matrix is that it is positive-semidefinite. This means that the eigenvalues are non-negative (and sum to 1, so we can assign them the meaning of proba …

Let $\rho$ be a density matrix for hilbert space of dimension $n$ (satisfying $\rho^\dagger = \rho$ and $\mathrm{tr}[\rho] =1$ and $\rho \geq 0$). Let $P$ be a projection operator. This means $P^2 = P …