# [CNOT GATE]how to go from a passage matrix acting on |C0>,C1>|T0>,T1> to the Cnot matrix acting on |C0T0>,C0T1>

In article A controlled-NOT gate for frequency-bin qubits, the authors built a passage matrix acting on the states $$T_0$$, $$T_1$$, $$C_0$$, $$C_1$$ and then they infered the famous two qubit matrix notation.

My question is how do they do that ?