  We show that any incoherent qubit channel could be decomposed into four
incoherent Kraus operators. The proof consists in showing existence of four
incoherent Kraus operators by decomposing the corresponding
Choi-Jamio\l{}kowski-Sudarshan matrix. We mention some applications of this
optimal decomposition. We also show that the Kraus rank and incoherent rank are
different even for qubit channel.
