Quantum systems: three-level vs qutrit Is there a difference between a three-level atomic system and a qutrit? If yes, please tell me what it is and how to relate both quantum systems.
 A: In a qutrit, every transition between pairs of levels is independent, in the sense that $\vert 1\rangle \leftrightarrow \vert 2\rangle$ is independent from $\vert 1\rangle \leftrightarrow \vert 3\rangle $ which is independent from $\vert 2\rangle\leftrightarrow \vert 3\rangle$.
Thus, not every three-level system is a qutrit.  For instance, the angular momentum states with $\ell=1$ do not form a qutrit if we restrict the observables to angular momentum operators, since, for instance the matrix elements $\langle 1,-1\vert L_- \vert 1,0\rangle =
\langle 1,0\vert L_-\vert 1,1\rangle=\sqrt{2}$, i.e. the transitions between adjacent levels are not independent.  In addition, a pulse resonant for the $m=-1\to m=0$ transition is also resonant for the $m=0\to m=1$ transition: in the case of $\ell=1$ states, not very transition can be accessed independently so it's NOT a true qutrit.  
Unfortunately too many people do confuse a spin triplet for a true qutrit.  This is because the states
$\{\vert 1,m\rangle\}$ do span the space, but the difficulty is with the operators: when restricted to angular momentum operators, not every transition can be accessed separately.  You need to use the full set $su(3)$ operators acting between basis states to properly described a qutrit.
An important and useful way to see the difference between angular momentum and $su(3)$ operators is that the standard ladder operators in $su(3)$ connect only 1 pair of states, whereas angular momentum operators connect two pairs of states when $\ell=1$.
