This is somewhat a simple question. If we generate random channels using QuTiP, say that we generate a channel that acts on a 3-dim space using rand_super_bcsz(3) we get the following output as an instance,
Quantum object: dims = [[[3], [3]], [[3], [3]]], shape = (9, 9), type = super, isherm = False
Qobj data =
[[ 0.4438227 -3.79097986e-18j -0.04399115-3.07652240e-02j
-0.02547192+1.05213719e-03j -0.04399115+3.07652240e-02j
0.60706348-6.62835587e-17j -0.00458043+1.78828982e-02j
-0.02547192-1.05213719e-03j -0.00458043-1.78828982e-02j
0.43515102+2.89297405e-18j]
[-0.09695176+2.76107000e-01j -0.07594095+6.68822348e-02j
-0.11336127+3.86103563e-02j -0.06884106-5.72774291e-02j
0.04316332-2.09920166e-02j -0.25213549-2.67443003e-03j
-0.01955145+1.04494620e-02j -0.00800644-1.33683273e-01j
0.07160461+1.80430664e-01j]
[ 0.02806479-1.50147404e-02j 0.04969676+6.29521473e-02j
-0.0013349 +6.76043940e-02j -0.24811695+1.48083015e-01j
0.0766544 +1.19882749e-01j -0.0194107 +1.12281022e-01j
0.06985962-5.32365584e-02j -0.00152423+1.90536335e-02j
-0.01481072+1.34097571e-01j]
[-0.09695176-2.76107000e-01j -0.06884106+5.72774291e-02j
-0.01955145-1.04494620e-02j -0.07594095-6.68822348e-02j
0.04316332+2.09920166e-02j -0.00800644+1.33683273e-01j
-0.11336127-3.86103563e-02j -0.25213549+2.67443003e-03j
0.07160461-1.80430664e-01j]
[ 0.2915839 -2.62745139e-18j 0.07037888+3.10378230e-02j
0.06150088+3.33975343e-02j 0.07037888-3.10378230e-02j
0.15073871-3.29013712e-17j -0.06243235-4.51956412e-02j
0.06150088-3.33975343e-02j -0.06243235+4.51956412e-02j
0.37925264-8.46143899e-18j]
[ 0.01381757+7.23661016e-03j -0.00093905-5.25495866e-02j
0.0618214 -8.31114284e-02j -0.02882676+2.64096709e-02j
-0.00493698+2.26155011e-02j -0.00076473-9.91256393e-04j
0.05647629-1.43073041e-01j -0.00814847-9.71055694e-02j
0.08556717-1.52263515e-02j]
[ 0.02806479+1.50147404e-02j -0.24811695-1.48083015e-01j
0.06985962+5.32365584e-02j 0.04969676-6.29521473e-02j
0.0766544 -1.19882749e-01j -0.00152423-1.90536335e-02j
-0.0013349 -6.76043940e-02j -0.0194107 -1.12281022e-01j
-0.01481072-1.34097571e-01j]
[ 0.01381757-7.23661016e-03j -0.02882676-2.64096709e-02j
0.05647629+1.43073041e-01j -0.00093905+5.25495866e-02j
-0.00493698-2.26155011e-02j -0.00814847+9.71055694e-02j
0.0618214 +8.31114284e-02j -0.00076473+9.91256393e-04j
0.08556717+1.52263515e-02j]
[ 0.2645934 -3.25260652e-18j -0.02638774-2.72599009e-04j
-0.03602896-3.44496715e-02j -0.02638774+2.72599009e-04j
0.24219781-1.99493200e-17j 0.06701278+2.73127429e-02j
-0.03602896+3.44496715e-02j 0.06701278-2.73127429e-02j
0.18559633+7.80625564e-18j]]
Now, my question is simply that I would like to read this output in the following sense. If we consider a channel $\Lambda$ we can define this in terms of $\Lambda_{ab}^{cd}$ using $$\Lambda(\vert a \rangle \langle b \vert ) = \sum_{cd}\Lambda_{cd}^{ab}\vert c \rangle \langle d \vert $$
so my question is how to read the values $\Lambda^{ab}_{cd}$ from the outputs of these QuTiP random generators, or more generaly, any channel. My attempt goes as follows: In this case we have that each dummy variable takes $3$ possible values. It seems that each row corresponds to a choice of pair $(ab)$ or of a pair $(cd)$. Clearly if we let $a=0,1,2$ etc we have that $\Lambda_{00}^{00} = 0.4438227 -3.79097986e-18j$. Then, $\Lambda_{01}^{00} = -0.04399115-3.07652240e-02j$, $\Lambda_{02}^{00} = -0.02547192+1.05213719e-03j$ and so on?
