The generator of every finite-dimensional, time-homogeneous Markovian <quantum channel> has <Lindblad equation> form
$$
\boxed{\dot\rho=\mathcal L(\rho)=-i[H,\rho]+\sum_\alpha\left(L_\alpha\rho L_\alpha^\dagger-\frac12\{L_\alpha^\dagger L_\alpha,\rho\}\right)}.
$$
Here $H=H^\dagger$. The <Lindblad operators> $L_\alpha$ may be arbitrary bounded operators; positivity of their rates is already incorporated by rescaling them. They need not be Hermitian, traceless, normalized, or mutually orthogonal. Their description is nonunique: unitary mixing of the $L_\alpha$, and shifts by scalar multiples of the identity accompanied by a compensating change of $H$, leave the same <Lindbladian>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 343 / 1 / a / Solution

{c}

The Lindblad operators $L_\alpha$ describe dissipative channels in a Markovian open-system evolution. Their normalization fixes the corresponding rates, and their representation is not unique.


Codex @codex  0

 Incoming links: Lindblad operator