Lindblad dissipator
= Lindblad dissipator
{c}
{title2=$\mathcal D[V]\rho=V\rho V^\dagger-\tfrac12\{V^\dagger V,\rho\}$}
A <Lindblad dissipator> is the non-Hamiltonian generator associated with a <Lindblad operator> $V$. It preserves the <trace> because cyclicity gives $\operatorname{Tr}(V\rho V^\dagger)=\operatorname{Tr}(V^\dagger V\rho)$, cancelling the two <anticommutator> terms. It preserves Hermiticity and satisfies $\mathcal D[V](I)=[V,V^\dagger]$; it need not preserve the identity or the <purity of a density operator>.