$\newcommand{\ket}[1]{|{#1}\rangle}\newcommand{\bra}[1]{\langle{#1}|}$ Si $\boldsymbol{A}$ y $\boldsymbol{B}$ son dos matrices de dimensión $2\times 2$ se tiene que \begin{align*} \boldsymbol{A} \otimes \boldsymbol{B} = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} \otimes \begin{bmatrix} b_{11} & b_{12}\\ b_{21} & b_{22} \end{bmatrix} = \begin{bmatrix} a_{11} b_{11} & a_{11} b_{12} & a_{12} b_{11} & a_{12} b_{12} \\ a_{11} b_{21} & a_{11} b_{22} & a_{12} b_{21} & a_{12} b_{22} \\ a_{21} b_{11} & a_{21} b_{12} & a_{22} b_{11} & a_{22} b_{12} \\ a_{21} b_{21} & a_{21} b_{22} & a_{22} b_{21} & a_{22} b_{22} \end{bmatrix}. \end{align*}
% El comando Matlab que realiza el producto de Kroenecker es kron(A,B):
A = [0 1; 2 3]
B = [10 11; 12 13]
A_kron_B = kron(A,B)
A =
0 1
2 3
B =
10 11
12 13
A_kron_B =
0 0 10 11
0 0 12 13
20 22 30 33
24 26 36 39