  In this paper, we consider the dynamical modeling of a class of quantum
network systems consisting of qubits. Qubit probes are employed to measure a
set of selected nodes of the quantum network systems. For a variety of
applications, a state space model is a useful way to model the system dynamics.
To construct a state space model for a quantum network system, the major task
is to find an accessible set containing all of the operators coupled to the
measurement operators. This paper focuses on the generation of a proper
accessible set for a given system and measurement scheme. We provide analytic
results on simplifying the process of generating accessible sets for systems
with a time-independent Hamiltonian. Since the order of elements in the
accessible set determines the form of state space matrices, guidance is
provided to effectively arrange the ordering of elements in the state vector.
Defining a system state according to the accessible set, one can develop a
state space model with a special pattern inherited from the system structure.
As a demonstration, we specifically consider a typical 1D-chain system with
several common measurements, and employ the proposed method to determine its
accessible set.
