  The information of quantum pathways can be extracted in the framework of the
Hamiltonian-encoding and Observable-decoding method. For closed quantum
systems, only off-diagonal elements of the Hamiltonian in the Hilbert space is
required to be encoded to obtain the desired transitions. For open quantum
systems, environment-related terms will appear in the diagonal elements of the
Hamiltonian in the Liouville space. Therefore, diagonal encodings have to be
performed to differentiate different pathways, which will lead to self-to-self
transitions and inconsistency of pathway amplitudes with Dyson expansion. In
this work, a well-designed transformation is proposed to avoid the
counter-intuitive transitions and the inconsistency, with or without control
fields. A three-level open quantum system is employed for illustration, and
numerical simulations show that the method are consistent with Dyson expansion.
