Choi matrix in QETLAB

Question

I am using QETLAB, a package for working with quantum information theory in Matlab and I have some doubts. I am trying to calculate diamond norms using such for some quantum channels. However, when doing so, it is said that a superoperator must be the input to the function. I know the Kraus representation of the channels I am testing, so I am not sure how to get the superoperator form of such. In the example they put in their wiki for their diamond norm they use a function called ChoiMatrix that calculates the Choi matrix of a supeorperator, but I am not sure if inputing the Kraus operators there will give me what I need.

An insight about the usage of the functions would be helpful, so as the relationship between superoperators, Kraus operators and Choi matrices.

Answer 1

QETLAB usually deals with channels as Choi operators. You can convert your Kraus operators to the Choi matrix by providing the Kraus operators as a cell array. Example with the amplitude damping channel below.

>> damp = 0.3;
>> K = { diag([1,sqrt(1-damp)]); [0,sqrt(damp);0,0] };
>> ChoiMatrix(K)

ans =

    1.0000         0         0    0.8367
         0         0         0         0
         0         0    0.3000         0
    0.8367         0         0    0.7000